Documentation improvements: Fix typos, grammar, and outdated references

benchmarks/AstroChem/astrochem.jmd

@@ -292,7 +292,7 @@ tspan = (0.0, 1e6*seconds_per_year)
 
 params = [dust2gas => 0.01, radiation_field => 1e-1, cosmic_ionisation_rate => 1e-17]
 
-println("Lets try to solve the ODE:")
+println("Attempting to solve the ODE...")
 
 sys = convert(ODESystem, complete(system))
 # oprob = ODEProblemExpr(sys, [], tspan, params)
@@ -302,7 +302,7 @@ ssys = structural_simplify(sys)
 
 ```julia
 oprob = ODEProblem(ssys, [], tspan, params)
-println("Created the ODEproblem.")
+println("ODEProblem created successfully.")
 sol = solve(oprob, Rodas5()) # Rodas5()) # Tsit5()
 
 # Generate a solution using high precision arithmetic
@@ -385,15 +385,15 @@ tspan = (0.0, 1e6*seconds_per_year)
 
 params = [dust2gas => 0.01, radiation_field => 1e-1, cosmic_ionisation_rate => 1e-17]
 
-println("Lets try to solve the ODE:")
+println("Attempting to solve the ODE...")
 
 sys = convert(ODESystem, complete(system))
 # oprob = ODEProblemExpr(sys, [], tspan, params)
 
 ssys = structural_simplify(sys)
 
 oprob = ODEProblem(ssys, [], tspan, params)
-println("Created the ODEproblem.")
+println("ODEProblem created successfully.")
 refsol = solve(oprob, Rodas5P(), abstol = 1e-14, reltol = 1e-14)
 ```
 

benchmarks/BayesianInference/DiffEqBayesLorenz.jmd

@@ -151,7 +151,7 @@ model = fitlv(data, sprob)
 ## Conclusion
 
 Due to the chaotic nature of Lorenz Equation, it is a very hard problem to estimate as it has the property of exponentially increasing errors.
-Its uncertainty plot points to its chaotic behaviour and goes awry for different values of tolerance, we use 1e-8 as the tolerance as it makes its uncertainty small enough to be trusted in `(0,30)` time span.
+Its uncertainty plot demonstrates chaotic behavior and exhibits instability for different tolerance values. We use 1e-8 as the tolerance as it makes its uncertainty small enough to be trusted in the `(0,30)` time span.
 
 ```julia, echo = false
 using SciMLBenchmarks

benchmarks/Bio/BCR.jmd

@@ -48,7 +48,7 @@ show(to)
 
 ```julia
 @show numspecies(rn) # Number of ODEs
-@show numreactions(rn) # Apprx. number of terms in the ODE
+@show numreactions(rn) # Approx. number of terms in the ODE
 @show length(parameters(rn)); # Number of Parameters
 ```
 

benchmarks/Bio/egfr_net.jmd

@@ -46,7 +46,7 @@ show(to)
 
 ```julia
 @show numspecies(rn) # Number of ODEs
-@show numreactions(rn) # Apprx. number of terms in the ODE
+@show numreactions(rn) # Approx. number of terms in the ODE
 @show length(parameters(rn)); # Number of Parameters
 ```
 

benchmarks/Bio/fceri_gamma2.jmd

@@ -45,7 +45,7 @@ oprob_sparse = ODEProblem{true, SciMLBase.FullSpecialize}(
 
 ```julia
 @show numspecies(rn) # Number of ODEs
-@show numreactions(rn) # Apprx. number of terms in the ODE
+@show numreactions(rn) # Approx. number of terms in the ODE
 @show length(parameters(rn)); # Number of Parameters
 ```
 

benchmarks/Bio/multisite2.jmd

@@ -45,7 +45,7 @@ show(to)
 
 ```julia
 @show numspecies(rn) # Number of ODEs
-@show numreactions(rn) # Apprx. number of terms in the ODE
+@show numreactions(rn) # Approx. number of terms in the ODE
 @show length(parameters(rn)); # Number of Parameters
 ```
 

benchmarks/Bio/multistate.jmd

@@ -45,7 +45,7 @@ show(to)
 
 ```julia
 @show numspecies(rn) # Number of ODEs
-@show numreactions(rn) # Apprx. number of terms in the ODE
+@show numreactions(rn) # Approx. number of terms in the ODE
 @show length(parameters(rn)); # Number of Parameters
 ```
 

benchmarks/ParameterEstimation/FitzHughNagumoParameterEstimation.jmd

@@ -111,7 +111,7 @@ obj_short = build_loss_objective(prob_short, Vern9(), L2Loss(t_short, data_short
     tstops = t_short, reltol = 1e-9, abstol = 1e-9)
 optprob = OptimizationProblem(obj_short, glo_init, lb = first.(glo_bounds), ub = last.(glo_bounds))
 @btime res1 = solve(optprob, BBO_adaptive_de_rand_1_bin(), maxiters = 7e3)
-# using the moe accurate Vern9() reduces the fitness marginally and leads to some increase in time taken
+# using the more accurate Vern9() reduces the fitness marginally and leads to some increase in time taken
 ```
 
 ## Using NLopt

benchmarks/ParameterEstimation/LotkaVolterraParameterEstimation.jmd

@@ -113,7 +113,7 @@ obj_short = build_loss_objective(prob_short, Vern9(), L2Loss(t_short, data_short
     tstops = t_short, reltol = 1e-9, abstol = 1e-9)
 optprob = OptimizationProblem(obj_short, loc_init, lb = first.(loc_bounds), ub = last.(loc_bounds))
 @btime res1 = solve(optprob, BBO_adaptive_de_rand_1_bin(); maxiters = 7e3)
-# using the moe accurate Vern9() reduces the fitness marginally and leads to some increase in time taken
+# using the more accurate Vern9() reduces the fitness marginally and leads to some increase in time taken
 ```
 
 # Using NLopt
@@ -146,7 +146,7 @@ opt = Opt(:GN_ESCH, 4)
 @btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
 ```
 
-Now local optimization algorithms are used to check the global ones, these use the local constraints, different initial values and time step
+Now local optimization algorithms are used to verify the global ones. These use the local constraints, different initial values and time step.
 
 ```julia
 optprob = OptimizationProblem(obj_short, loc_init, lb = first.(loc_bounds), ub = last.(loc_bounds))
@@ -199,7 +199,7 @@ opt = Opt(:LD_TNEWTON_PRECOND_RESTART, 4)
 
 ## Now the longer problem is solved for a global solution
 
-Vern9 solver with reltol=1e-9 and abstol=1e-9 is used and the dataset is increased to 3000 observations per variable with the same integration time step of 0.01.
+The Vern9 solver with reltol=1e-9 and abstol=1e-9 is used, and the dataset is increased to 3000 observations per variable with the same integration time step of 0.01.
 
 ```julia
 t_concrete = collect(0.0:dt:tf)
@@ -259,7 +259,7 @@ opt = Opt(:LD_SLSQP, 4)
 
 # Conclusion
 
-In general we observe that lower tolerance lead to higher accuracy but too low tolerance could affect the convergence time drastically. Also fitting a shorter timespan seems to be easier in comparison (quite intuitively). NLOpt methods seem to give great accuracy in the shorter problem with a lot of the algorithms giving 0 fitness, BBO performs very well on it with marginal change with `tol` values. In case of global optimization of the longer problem  there is some difference in the performance amongst the algorithms with `LD_SLSQP` `GN_ESCH` `GN_ISRES` `GN_ORIG_DIRECT_L` performing among the worse, BBO also gives a bit high fitness in comparison. QuadDIRECT gives accurate results in the case of the shorter problem but doesn't perform very well in the longer problem case.
+In general we observe that lower tolerances lead to higher accuracy but too low tolerance could affect the convergence time drastically. Also fitting a shorter timespan seems to be easier in comparison (quite intuitively). NLOpt methods seem to give great accuracy in the shorter problem with a lot of the algorithms giving 0 fitness, BBO performs very well on it with marginal change with `tol` values. In the case of global optimization for the longer problem, there is some difference in performance among the algorithms with `LD_SLSQP` `GN_ESCH` `GN_ISRES` `GN_ORIG_DIRECT_L` performing among the worst, BBO also gives a bit high fitness in comparison. QuadDIRECT gives accurate results in the case of the shorter problem but doesn't perform very well in the longer problem case.
 
 ```julia, echo = false
 using SciMLBenchmarks

benchmarks/StiffODE/Hires.jmd

@@ -49,8 +49,7 @@ plot(sol, tspan = (0.0, 5.0))
 ## Omissions
 
 The following were omitted from the tests due to convergence failures. ODE.jl's
-adaptivity is not able to stabilize its algorithms, while
-GeometricIntegratorsDiffEq has not upgraded to Julia 1.0.
+adaptivity is not able to stabilize its algorithms.
 GeometricIntegrators.jl's methods used to either fail to converge at
 comparable dts (or on some computers had errors due to type conversions).
 

benchmarks/StiffODE/Orego.jmd

@@ -36,8 +36,7 @@ plot(sol,yscale=:log10)
 ## Omissions and Tweaking
 
 The following were omitted from the tests due to convergence failures. ODE.jl's
-adaptivity is not able to stabilize its algorithms, while
-GeometricIntegratorsDiffEq has not upgraded to Julia 1.0.
+adaptivity is not able to stabilize its algorithms.
 GeometricIntegrators.jl's methods used to either fail to converge at
 comparable dts (or on some computers had errors due to type conversions).
 

benchmarks/StiffODE/Pollution.jmd

@@ -218,8 +218,7 @@ plot(sol,tspan=(0.0,5.0))
 ## Omissions
 
 The following were omitted from the tests due to convergence failures. ODE.jl's
-adaptivity is not able to stabilize its algorithms, while
-GeometricIntegratorsDiffEq has not upgraded to Julia 1.0.
+adaptivity is not able to stabilize its algorithms.
 GeometricIntegrators.jl's methods used to either fail to converge at
 comparable dts (or on some computers had errors due to type conversions).
 

benchmarks/StiffODE/ROBER.jmd

@@ -33,8 +33,7 @@ plot(sol,labels=["y1","y2","y3"])
 ## Omissions And Tweaking
 
 The following were omitted from the tests due to convergence failures. ODE.jl's
-adaptivity is not able to stabilize its algorithms, while
-GeometricIntegratorsDiffEq has not upgraded to Julia 1.0.
+adaptivity is not able to stabilize its algorithms.
 GeometricIntegrators.jl's methods used to either fail to converge at
 comparable dts (or on some computers had errors due to type conversions).
 

benchmarks/StiffODE/VanDerPol.jmd

@@ -38,8 +38,7 @@ plot(sol)
 ## Omissions And Tweaking
 
 The following were omitted from the tests due to convergence failures. ODE.jl's
-adaptivity is not able to stabilize its algorithms, while
-GeometricIntegratorsDiffEq has not upgraded to Julia 1.0.
+adaptivity is not able to stabilize its algorithms.
 GeometricIntegrators.jl's methods used to either fail to converge at
 comparable dts (or on some computers had errors due to type conversions).