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The solution of high-order nonlinear ordinary differential equations by Chebyshev series. (English) Zbl 1209.65068

Summary: By the use of the Chebyshev series, a direct computational method for solving higher order nonlinear differential equations is developed. This method transforms the nonlinear differential equation into a matrix equation, which corresponds to a system of nonlinear algebraic equations with unknown Chebyshev coefficients, via Chebyshev collocation points. The solution of this system yields the Chebyshev coefficients of the solution function. An algorithm for this nonlinear system is also proposed. The method is valid for both initial-value and boundary-value problems. Several examples are presented to illustrate the accuracy and effectiveness of the method.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34B15 Nonlinear boundary value problems for ordinary differential equations
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
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