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Zbl 0948.65071
Guo, Benyu
Jacobi spectral approximations to differential equations on the half line. (English)
[J] J. Comput. Math. 18, No.1, 95-112 (2000). ISSN 0254-9409; ISSN 1991-7139/e

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.
[Yuri V.Rogovchenko (Mersin)]

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
65L20 Stability of numerical methods for ODE
35Q53 KdV-like equations
65L60 Finite numerical methods for ODE
34B15 Nonlinear boundary value problems of ODE

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

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