Jacobi spectral approximations to differential equations on the half line. (English) Zbl 0948.65071

Guo, Benyu

J. Comput. Math. 18, No. 1, 95-112 (2000).

For the numerical study of differential equations on the half-line, the reduction to certain problems on a finite interval is often used. Since the coefficients of the resulting equations degenerate only at one of the endpoints, the use of Jacobi polynomials is suggested by the author for the approximation of the coefficients, and the corresponding mathematical apparatus is developed. The paper concludes with some applications, and the question of stability and convergence of the proposed schemes is addressed for the well-known nonlinear Burgers equation.

Reviewer: Yuri V.Rogovchenko (Mersin)

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations
35Q53	KdV equations (Korteweg-de Vries equations)
65L60	Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

Jacobi polynomials; weighted inequalities; orthogonal projections; differential equations on the half-line; stability; convergence; nonlinear Burgers equation