Collocation-continuation technique for solving nonlinear ordinary boundary value problems
The authors report a method, an algorithm and illustrate numerical examples to solve a Dirichlet boundary value problem for a particular second-order nonlinear ordinary differential equation. The discretization of the problem is done by the Legendre collocation method resulting in a system of nonlinear algebraic equations. The latter is then solved by a continuation method, which does not require an initial approximation.
two-point Dirichlet boundary value problems
second-order nonlinear ordinary differential equations
scientific article; zbMATH DE number 1391569