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Collocation method via Jacobi polynomials for solving nonlinear ordinary differential equations. (English) Zbl 1221.65173
Summary: We extend a collocation method for solving a nonlinear ordinary differential equation (ODE) via Jacobi polynomials. To date, researchers usually use Chebyshev or Legendre collocation method for solving problems in chemistry, physics, and so forth. Choosing the optimal polynomial for solving every ODEs problem depends on many factors, for example, smoothing continuously and other properties of the solutions. In this paper, we show intuitionally that in some problems choosing other members of Jacobi polynomials gives better result compared to Chebyshev or Legendre polynomials.
MSC:
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE