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Documentation improvements: grammar and clarity fixes
Fixed several grammar and clarity issues across documentation files: - Fixed missing space after `TwoPointBVProblem` in bvp_example.md - Improved sentence structure for initial guess description in bvp_example.md - Changed "shooting method" to "shooting methods" for parallel construction - Fixed subject-verb agreement: "supported" -> "supports" in index.md - Fixed verb tense consistency in overview.md: "choose" -> "chooses" - Fixed subject-verb agreement: "is defined" -> "are defined" in overview.md - Fixed subject-verb agreement: "hold" -> "holds" in overview.md - Improved clarity: "option mutating" -> "optional mutating" in problem.md - Fixed subject-verb agreement: "have that" -> "has" in problem.md - Removed redundant word "here" in getting_started.md These changes improve readability and grammatical correctness without altering any technical content or code examples. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>
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docs/src/basics/overview.md

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@@ -44,11 +44,11 @@ to dispatch to the right methods. The common interface for calling the solvers i
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sol = solve(prob, alg; kwargs)
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```
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Into the command, one passes the differential equation problem that they defined
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`prob`, optionally choose an algorithm `alg` (a default is given if not
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chosen), and change the properties of the solver using keyword arguments. The common
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arguments which are accepted by most methods is defined in [the common solver options manual page](@ref solver_options).
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The solver returns a solution object `sol` which hold all the details for the solution.
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Into the command, one passes the differential equation problem that they defined,
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`prob`, optionally chooses an algorithm `alg` (a default is given if not
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chosen), and changes the properties of the solver using keyword arguments. The common
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arguments which are accepted by most methods are defined in [the common solver options manual page](@ref solver_options).
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The solver returns a solution object `sol` which holds all the details for the solution.
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## Analyzing the Solution
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docs/src/basics/problem.md

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in-place form which, as its output, mutates `du`. Whatever is returned is simply
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ignored. Similarly, for OOP we have the form `du=f(u,p,t)` which uses the return.
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Each of the problem types have that the first argument is the option mutating
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Each of the problem types has the first argument as the optional mutating
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argument. The SciMLBase system will automatically determine the functional
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form and place a specifier `isinplace` on the function to carry as type information
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whether the function defined for this `DEProblem` is in-place. However, every

docs/src/getting_started.md

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Plots.plot(sol, idxs = (0, 2))
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```
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Note that here “variable 0 corresponds to the independent variable (time).
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Note that "variable 0" corresponds to the independent variable ("time").
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## Defining Parameterized Functions
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docs/src/index.md

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from [the JuliaLang site](https://julialang.org/downloads/) and add it to your path. The download and
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installation of DifferentialEquations.jl will happen on the first invocation of `diffeqr::diffeq_setup()`.
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Currently, use from R supported a subset of DifferentialEquations.jl which is documented
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Currently, use from R supports a subset of DifferentialEquations.jl which is documented
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[through CRAN](https://cran.r-project.org/web/packages/diffeqr/index.html).
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### Video Tutorial

docs/src/tutorials/bvp_example.md

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There are two problem types available:
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- A problem type for general boundary conditions `BVProblem` (including conditions that may be anywhere/ everywhere on the integration interval, aka multi-points BVP).
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- A problem type for boundaries that are specified at the beginning and the end of the integration interval `TwoPointBVProblem`(aka two-points BVP)
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- A problem type for boundaries that are specified at the beginning and the end of the integration interval `TwoPointBVProblem` (aka two-points BVP)
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The boundary conditions are specified by a function that calculates the residual in-place from the problem solution, such that the residual is ``\vec{0}`` when the boundary condition is satisfied.
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Plots.plot(sol1)
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```
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The third argument of `BVProblem` or `TwoPointBVProblem` is the initial guess of the solution, which can be specified as a `Vector`, a `Function` of `t` or solution object from previous solving, in this example the initial guess is set as a `Vector`.
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The third argument of `BVProblem` or `TwoPointBVProblem` is the initial guess of the solution, which can be specified as a `Vector`, a `Function` of `t`, or a solution object from previous solving. In this example, the initial guess is set as a `Vector`.
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```@example bvp
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import OrdinaryDiffEq as ODE
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sol3 = BVP.solve(bvp3, BVP.Shooting(ODE.Vern7()))
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```
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The initial guess can also be supplied via a function of `t` or a previous solution type, this is especially handy for parameter analysis.
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We changed `u` to `sol` to emphasize the fact that in this case, the boundary condition can be written on the solution object. Thus, all the features on the solution type such as interpolations are available when using both collocation and shooting method. (i.e. you can have a boundary condition saying that the maximum over the interval is `1` using an optimization function on the continuous output).
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The initial guess can also be supplied via a function of `t` or a previous solution type, which is especially handy for parameter analysis.
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We changed `u` to `sol` to emphasize the fact that in this case, the boundary condition can be written on the solution object. Thus, all the features on the solution type such as interpolations are available when using both collocation and shooting methods (i.e., you can have a boundary condition saying that the maximum over the interval is `1` using an optimization function on the continuous output).
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```@example bvp
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Plots.plot(sol3)

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