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‎previews/PR49/.documenter-siteinfo.json‎

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{"documenter":{"documenter_version":"1.17.0","generation_timestamp":"2026-04-13T09:21:25","julia_version":"1.11.9"}}
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{"documenter":{"documenter_version":"1.17.0","generation_timestamp":"2026-04-13T09:22:55","julia_version":"1.11.9"}}

‎previews/PR49/generated/bratu/index.html‎

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copy(u₀), (dx, λ);
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algo = :cg
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)
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(11, 60160, 6.086180541247742e-5), t = 15.744614243)</code></pre><h2 id="Solving-with-a-fixed-forcing"><a class="docs-heading-anchor" href="#Solving-with-a-fixed-forcing">Solving with a fixed forcing</a><a id="Solving-with-a-fixed-forcing-1"></a><a class="docs-heading-anchor-permalink" href="#Solving-with-a-fixed-forcing" title="Permalink"></a></h2><pre><code class="language-julia hljs">_, stats = newton_krylov!(
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(11, 60160, 6.086180541247742e-5), t = 15.518938806)</code></pre><h2 id="Solving-with-a-fixed-forcing"><a class="docs-heading-anchor" href="#Solving-with-a-fixed-forcing">Solving with a fixed forcing</a><a id="Solving-with-a-fixed-forcing-1"></a><a class="docs-heading-anchor-permalink" href="#Solving-with-a-fixed-forcing" title="Permalink"></a></h2><pre><code class="language-julia hljs">_, stats = newton_krylov!(
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bratu!,
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copy(u₀), (dx, λ), similar(u₀);
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algo = :cg,
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forcing = Ariadne.Fixed(0.1)
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)
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(8, 56510, 2.773666992173675e-5), t = 5.218180044)</code></pre><h2 id="Solving-with-no-forcing"><a class="docs-heading-anchor" href="#Solving-with-no-forcing">Solving with no forcing</a><a id="Solving-with-no-forcing-1"></a><a class="docs-heading-anchor-permalink" href="#Solving-with-no-forcing" title="Permalink"></a></h2><pre><code class="language-julia hljs">_, stats = newton_krylov!(
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(8, 56510, 2.773666992173675e-5), t = 5.475078758)</code></pre><h2 id="Solving-with-no-forcing"><a class="docs-heading-anchor" href="#Solving-with-no-forcing">Solving with no forcing</a><a id="Solving-with-no-forcing-1"></a><a class="docs-heading-anchor-permalink" href="#Solving-with-no-forcing" title="Permalink"></a></h2><pre><code class="language-julia hljs">_, stats = newton_krylov!(
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bratu!,
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copy(u₀), (dx, λ), similar(u₀);
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algo = :cg,
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forcing = nothing
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)
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(8, 71652, 3.217114944736544e-6), t = 6.779912168)</code></pre><h2 id="Solve-using-GMRES-–-doesn&#39;t-converge"><a class="docs-heading-anchor" href="#Solve-using-GMRES-–-doesn&#39;t-converge">Solve using GMRES – doesn&#39;t converge</a><a id="Solve-using-GMRES-–-doesn&#39;t-converge-1"></a><a class="docs-heading-anchor-permalink" href="#Solve-using-GMRES-–-doesn&#39;t-converge" title="Permalink"></a></h2><pre><code class="language-julia hljs">_, stats = newton_krylov!(
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(8, 71652, 3.217114944736544e-6), t = 7.11768374)</code></pre><h2 id="Solve-using-GMRES-–-doesn&#39;t-converge"><a class="docs-heading-anchor" href="#Solve-using-GMRES-–-doesn&#39;t-converge">Solve using GMRES – doesn&#39;t converge</a><a id="Solve-using-GMRES-–-doesn&#39;t-converge-1"></a><a class="docs-heading-anchor-permalink" href="#Solve-using-GMRES-–-doesn&#39;t-converge" title="Permalink"></a></h2><pre><code class="language-julia hljs">_, stats = newton_krylov!(
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bratu!,
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copy(u₀), (dx, λ), similar(u₀);
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algo = :gmres,
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N = (J) -&gt; ilu(collect(J)), # Assembles the full Jacobian
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krylov_kwargs = (; ldiv = true)
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)
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(8, 8, 3.216849217028634e-6), t = 8.341381859)</code></pre><h2 id="Solve-using-FGMRES-ILU-Preconditioner"><a class="docs-heading-anchor" href="#Solve-using-FGMRES-ILU-Preconditioner">Solve using FGMRES + ILU Preconditioner</a><a id="Solve-using-FGMRES-ILU-Preconditioner-1"></a><a class="docs-heading-anchor-permalink" href="#Solve-using-FGMRES-ILU-Preconditioner" title="Permalink"></a></h2><pre><code class="language-julia hljs">_, stats = newton_krylov!(
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(8, 8, 3.216849217028634e-6), t = 8.808901746)</code></pre><h2 id="Solve-using-FGMRES-ILU-Preconditioner"><a class="docs-heading-anchor" href="#Solve-using-FGMRES-ILU-Preconditioner">Solve using FGMRES + ILU Preconditioner</a><a id="Solve-using-FGMRES-ILU-Preconditioner-1"></a><a class="docs-heading-anchor-permalink" href="#Solve-using-FGMRES-ILU-Preconditioner" title="Permalink"></a></h2><pre><code class="language-julia hljs">_, stats = newton_krylov!(
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copy(u₀), (dx, λ), similar(u₀);
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algo = :fgmres,
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N = (J) -&gt; ilu(collect(J)), # Assembles the full Jacobian
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krylov_kwargs = (; ldiv = true)
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)
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(8, 8, 3.2061685998371007e-6), t = 7.551376144)</code></pre><h2 id="Solve-using-FGMRES-GMRES-Preconditioner"><a class="docs-heading-anchor" href="#Solve-using-FGMRES-GMRES-Preconditioner">Solve using FGMRES + GMRES Preconditioner</a><a id="Solve-using-FGMRES-GMRES-Preconditioner-1"></a><a class="docs-heading-anchor-permalink" href="#Solve-using-FGMRES-GMRES-Preconditioner" title="Permalink"></a></h2><pre><code class="language-julia hljs">struct GmresPreconditioner{JOp}
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(8, 8, 3.2061685998371007e-6), t = 8.048957564)</code></pre><h2 id="Solve-using-FGMRES-GMRES-Preconditioner"><a class="docs-heading-anchor" href="#Solve-using-FGMRES-GMRES-Preconditioner">Solve using FGMRES + GMRES Preconditioner</a><a id="Solve-using-FGMRES-GMRES-Preconditioner-1"></a><a class="docs-heading-anchor-permalink" href="#Solve-using-FGMRES-GMRES-Preconditioner" title="Permalink"></a></h2><pre><code class="language-julia hljs">struct GmresPreconditioner{JOp}
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J::JOp
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itmax::Int
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end
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algo = :fgmres,
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N = (J) -&gt; GmresPreconditioner(J, 5),
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)
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(12, 11973, 9.343815298545975e-5), t = 77.711717291)</code></pre><h2 id="Explodes.."><a class="docs-heading-anchor" href="#Explodes..">Explodes..</a><a id="Explodes..-1"></a><a class="docs-heading-anchor-permalink" href="#Explodes.." title="Permalink"></a></h2><pre><code class="language-julia hljs">newton_krylov!(
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stats</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(solved = true, stats = Ariadne.Stats(12, 11973, 9.343815298545975e-5), t = 64.314852067)</code></pre><h2 id="Explodes.."><a class="docs-heading-anchor" href="#Explodes..">Explodes..</a><a id="Explodes..-1"></a><a class="docs-heading-anchor-permalink" href="#Explodes.." title="Permalink"></a></h2><pre><code class="language-julia hljs">newton_krylov!(
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copy(u₀), (dx, λ), similar(u₀);
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algo = :cgls, # Cgne
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verbose = 1,
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algo = :bicgstab, # L=2
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η_max = nothing
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)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../bratu_ka/">Bratu – KernelAbstractions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.17.0 on <span class="colophon-date" title="Monday 13 April 2026 09:21">Monday 13 April 2026</span>. Using Julia version 1.11.9.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../bratu_ka/">Bratu – KernelAbstractions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.17.0 on <span class="colophon-date" title="Monday 13 April 2026 09:22">Monday 13 April 2026</span>. Using Julia version 1.11.9.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

‎previews/PR49/generated/bratu_ka/index.html‎

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lines!(ax, abs2.(uₖ .- reference))
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fig
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end</code></pre><img src="baeaeeab.png" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../bratu/">« Bratu – 1D</a><a class="docs-footer-nextpage" href="../simple/">Simple »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.17.0 on <span class="colophon-date" title="Monday 13 April 2026 09:21">Monday 13 April 2026</span>. Using Julia version 1.11.9.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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end</code></pre><img src="baeaeeab.png" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../bratu/">« Bratu – 1D</a><a class="docs-footer-nextpage" href="../simple/">Simple »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.17.0 on <span class="colophon-date" title="Monday 13 April 2026 09:22">Monday 13 April 2026</span>. Using Julia version 1.11.9.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

‎previews/PR49/generated/bvp/index.html‎

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return (; bvpout, tv, stats)
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end
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BVP_solve()</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(bvpout = [2.118836065354025, 4.0280052186324184e-11, 2.119050941817249, 0.017190114960574022, 2.119463196460868, 0.015790245636440253, 2.120005366547538, 0.02758335479467456, 2.120786563965859, 0.034912439947959714 … 1.8666598203578283e-9, 2.2197193441954643e-8, 8.104302904569911e-10, 2.206397624880973e-8, 1.948782984831248e-10, 2.295877639742203e-8, -6.205470008228236e-10, 2.4023175636286494e-8, -2.516291105889508e-10, 2.4412507318337302e-8], tv = [0.0, 0.025, 0.05, 0.075, 0.1, 0.125, 0.15, 0.175, 0.2, 0.225 … 19.775, 19.8, 19.825, 19.85, 19.875, 19.9, 19.925, 19.95, 19.975, 20.0], stats = (solved = true, stats = Ariadne.Stats(40, 34421, 1.23995890272197e-7), t = 39.247666988))</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../simple/">« Simple</a><a class="docs-footer-nextpage" href="../implicit/">Implicit »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.17.0 on <span class="colophon-date" title="Monday 13 April 2026 09:21">Monday 13 April 2026</span>. Using Julia version 1.11.9.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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BVP_solve()</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(bvpout = [2.118836065354025, 4.0280052186324184e-11, 2.119050941817249, 0.017190114960574022, 2.119463196460868, 0.015790245636440253, 2.120005366547538, 0.02758335479467456, 2.120786563965859, 0.034912439947959714 … 1.8666598203578283e-9, 2.2197193441954643e-8, 8.104302904569911e-10, 2.206397624880973e-8, 1.948782984831248e-10, 2.295877639742203e-8, -6.205470008228236e-10, 2.4023175636286494e-8, -2.516291105889508e-10, 2.4412507318337302e-8], tv = [0.0, 0.025, 0.05, 0.075, 0.1, 0.125, 0.15, 0.175, 0.2, 0.225 … 19.775, 19.8, 19.825, 19.85, 19.875, 19.9, 19.925, 19.95, 19.975, 20.0], stats = (solved = true, stats = Ariadne.Stats(40, 34421, 1.23995890272197e-7), t = 38.788689298))</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../simple/">« Simple</a><a class="docs-footer-nextpage" href="../implicit/">Implicit »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.17.0 on <span class="colophon-date" title="Monday 13 April 2026 09:22">Monday 13 April 2026</span>. Using Julia version 1.11.9.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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