Boundary-Value Problem
Types
LUSE_ENGR701_704_NumericalMethods.BoundaryValueProblems.BoundaryValueProblem — TypeBoundaryValueProblem(f, a, b, h, α, β, N)Structure of the boundary conditions to Boundary-Value Problem (BVP) differential equations.
Notes
Make sure the independent variable (e.g. time) is the first argument of f!
Functions
LUSE_ENGR701_704_NumericalMethods.BoundaryValueProblems.finite_difference_method — Methodfinite_difference_method(BVP[; method=:gauss_seidel, M=100, tol=10^-3])Solve BVP differential equations with Dirichlet boundary conditions by 2 IVP differential equations according to method ∈ {:jacobi, :gauss_seidel (default), :successive_relaxation, :newton_raphson} within numerical iterations, M and tolerance, tol.
Uses a Taylor polynomial with a first-order and a second-order IVP equations. Converges 𝒪(h²).
LUSE_ENGR701_704_NumericalMethods.BoundaryValueProblems.linear_shooting_method — Methodlinear_shooting_method(BVP)Solve a BVP differential equation with 2 IVP differential equations with in RK4 scheme.