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Approximate solutions of Fisher’s type equations with variable coefficients. (English) Zbl 1297.65126

Summary: The spectral collocation approximations based on Legendre polynomials are used to compute the numerical solution of time-dependent Fisher’s type problems. The spatial derivatives are collocated at a Legendre-Gauss-Lobatto interpolation nodes. The proposed method has the advantage of reducing the problem to a system of ordinary differential equations in time. The four-stage A-stable implicit Runge-Kutta scheme is applied to solve the resulted system of first order in time. Numerical results show that the Legendre-Gauss-Lobatto collocation method is of high accuracy and is efficient for solving the Fisher’s type equations. Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
35Q35 PDEs in connection with fluid mechanics
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