Solving Finite Difference Approximations to Nonlinear Two-Point Boundary Value Problems by a Homotopy Method

DOI10.1137/0901034zbMath0456.65025OpenAlexW2021131708MaRDI QIDQ3906318

Layne T. Watson

Publication date: 1980

Published in: SIAM Journal on Scientific and Statistical Computing (Search for Journal in Brave)

Full work available at URL: http://eprints.cs.vt.edu/archive/00000840/

zbMATH Keywords

numerical examplesfinite difference approximationshomotopy methodfixed point computationChow-Yorke algorithm

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10) Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (10)

On the solution of the polynomial systems arising in the discretization of certain ODEs ⋮ Solving spline-collocation approximations to nonlinear two-point boundary-value problems by a homotopy method ⋮ Approximation of the solution of certain nonlinear ODEs with linear complexity ⋮ Tracing multiple solution branches for nonlinear ordinary differential equations: Chebyshev and Fourier spectral methods and a degree-increasing spectral homotopy [DISH] ⋮ Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption ⋮ Engineering applications of the Chow-Yorke algorithm ⋮ Homotopy solution for nonlinear differential equations in wave propagation problems ⋮ Two-parameter homotopy method for nonlinear equations ⋮ Globally convergent homotopy methods: A tutorial ⋮ A homotopy continuation method for solving normal equations

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