@@ -6,7 +6,7 @@ for stage in (1, 2, 3, 5, 7)
66
77 @eval begin
88 """
9- $($ alg) (; nlsolve = NewtonRaphson(), jac_alg = BVPJacobianAlgorithm(), nested_nlsolve = false, nest_tol = 0.0,
9+ $($ alg) (; nlsolve = NewtonRaphson(), jac_alg = BVPJacobianAlgorithm(), nested_nlsolve = false, nest_tol = 0.0,
1010 defect_threshold = 0.1, max_num_subintervals = 3000)
1111
1212 $($ stage) th stage RadauIIa method.
@@ -107,18 +107,18 @@ for stage in (2, 3, 4, 5)
107107
108108 @eval begin
109109 """
110- $($ alg) (; nlsolve = NewtonRaphson(), jac_alg = BVPJacobianAlgorithm(), nested_nlsolve = false, nest_tol = 0.0,
110+ $($ alg) (; nlsolve = NewtonRaphson(), jac_alg = BVPJacobianAlgorithm(), nested_nlsolve = false, nest_tol = 0.0,
111111 defect_threshold = 0.1, max_num_subintervals = 3000)
112112
113113 $($ stage) th stage LobattoIIIa method.
114114
115115 ## Keyword Arguments
116116
117- - `nlsolve`: Internal Nonlinear solver. Any solver which conforms to the SciML
117+ - `nlsolve`: Internal Nonlinear solver. Any solver which conforms to the SciML
118118 `NonlinearProblem` interface can be used. Note that any autodiff argument for
119- the solver will be ignored and a custom jacobian algorithm will be used.
119+ the solver will be ignored and a custom jacobian algorithm will be used.
120120
121- - `optimize`: Internal Optimization solver. Any solver which conforms to the SciML
121+ - `optimize`: Internal Optimization solver. Any solver which conforms to the SciML
122122 `OptimizationProblem` interface can be used. Note that any autodiff argument for
123123 the solver will be ignored and a custom jacobian algorithm will be used.
124124
@@ -149,47 +149,46 @@ for stage in (2, 3, 4, 5)
149149
150150 ## References
151151
152- Reference for Lobatto and Radau methods:
153- ```bibtex
154- @Inbook{Jay2015,
155- author="Jay, Laurent O.",
156- editor="Engquist, Bj{\" o}rn",
157- title="Lobatto Methods",
158- booktitle = {Encyclopedia of {Applied} and {Computational} {Mathematics}},
159- year="2015",
160- publisher="Springer Berlin Heidelberg",
161- }
162- @incollection{engquist_radau_2015,
163- author = {Hairer, Ernst and Wanner, Gerhard},
164- title = {Radau {Methods}},
165- booktitle = {Encyclopedia of {Applied} and {Computational} {Mathematics}},
166- publisher = {Springer Berlin Heidelberg},
167- editor="Engquist, Bj{\" o}rn",
168- year = {2015},
169- }
170- ```
171- References for implementation of defect control, based on the `bvp5c` solver in MATLAB:
172- ```bibtex
173- @article{shampine_solving_nodate,
174- title = {Solving {Boundary} {Value} {Problems} for {Ordinary} {Differential} {Equations} in {Matlab} with bvp4c
175- author = {Shampine, Lawrence F and Kierzenka, Jacek and Reichelt, Mark W},
176- year = {2000},
177- }
178-
179- @article{kierzenka_bvp_2008,
180- title = {A {BVP} {Solver} that {Controls} {Residual} and {Error}},
181- author = {Kierzenka, J and Shampine, L F},
182- year = {2008},
183- }
184-
185- @article{russell_adaptive_1978,
186- title = {Adaptive {Mesh} {Selection} {Strategies} for {Solving} {Boundary} {Value} {Problems}},
187- journal = {SIAM Journal on Numerical Analysis},
188- author = {Russell, R. D. and Christiansen, J.},
189- year = {1978},
190- file = {Russell and Christiansen - 1978 - Adaptive Mesh Selection Strategies for Solving Bou.pdf:/Users/AXLRSN/Zotero/storage/HKU27A4T/Russell and Christiansen - 1978 - Adaptive Mesh Selection Strategies for Solving Bou.pdf:application/pdf},
191- }
192- ```
152+ Reference for Lobatto and Radau methods:
153+ ```bibtex
154+ @Inbook{Jay2015,
155+ author="Jay, Laurent O.",
156+ editor="Engquist, Bj{\" o}rn",
157+ title="Lobatto Methods",
158+ booktitle = {Encyclopedia of {Applied} and {Computational} {Mathematics}},
159+ year="2015",
160+ publisher="Springer Berlin Heidelberg",
161+ }
162+ @incollection{engquist_radau_2015,
163+ author = {Hairer, Ernst and Wanner, Gerhard},
164+ title = {Radau {Methods}},
165+ booktitle = {Encyclopedia of {Applied} and {Computational} {Mathematics}},
166+ publisher = {Springer Berlin Heidelberg},
167+ editor="Engquist, Bj{\" o}rn",
168+ year = {2015},
169+ }
170+ ```
171+ References for implementation of defect control, based on the `bvp5c` solver in MATLAB:
172+ ```bibtex
173+ @article{shampine_solving_nodate,
174+ title = {Solving {Boundary} {Value} {Problems} for {Ordinary} {Differential} {Equations} in {Matlab} with bvp4c
175+ author = {Shampine, Lawrence F and Kierzenka, Jacek and Reichelt, Mark W},
176+ year = {2000},
177+ }
178+
179+ @article{kierzenka_bvp_2008,
180+ title = {A {BVP} {Solver} that {Controls} {Residual} and {Error}},
181+ author = {Kierzenka, J and Shampine, L F},
182+ year = {2008},
183+ }
184+
185+ @article{russell_adaptive_1978,
186+ title = {Adaptive {Mesh} {Selection} {Strategies} for {Solving} {Boundary} {Value} {Problems}},
187+ journal = {SIAM Journal on Numerical Analysis},
188+ author = {Russell, R. D. and Christiansen, J.},
189+ year = {1978},
190+ }
191+ ```
193192 """
194193 Base. @kwdef struct $ (alg){N, O, J <: BVPJacobianAlgorithm , T} <: AbstractFIRK
195194 nlsolve:: N = nothing
@@ -208,7 +207,7 @@ for stage in (2, 3, 4, 5)
208207
209208 @eval begin
210209 """
211- $($ alg) (; nlsolve = NewtonRaphson(), jac_alg = BVPJacobianAlgorithm(), nested_nlsolve = false, nest_tol = 0.0,
210+ $($ alg) (; nlsolve = NewtonRaphson(), jac_alg = BVPJacobianAlgorithm(), nested_nlsolve = false, nest_tol = 0.0,
212211 defect_threshold = 0.1, max_num_subintervals = 3000)
213212
214213 $($ stage) th stage LobattoIIIb method.
@@ -310,7 +309,7 @@ for stage in (2, 3, 4, 5)
310309
311310 @eval begin
312311 """
313- $($ alg) (; nlsolve = NewtonRaphson(), jac_alg = BVPJacobianAlgorithm(), nested_nlsolve = false, nest_tol = 0.0,
312+ $($ alg) (; nlsolve = NewtonRaphson(), jac_alg = BVPJacobianAlgorithm(), nested_nlsolve = false, nest_tol = 0.0,
314313 defect_threshold = 0.1, max_num_subintervals = 3000)
315314
316315 $($ stage) th stage LobattoIIIc method.
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