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Jacobi spectral approximations to differential equations on the half line. (English) Zbl 0948.65071
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.
MSC:
65L10Boundary value problems for ODE (numerical methods)
65L20Stability and convergence of numerical methods for ODE
35Q53KdV-like (Korteweg-de Vries) equations
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34B15Nonlinear boundary value problems for ODE