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Numerical algorithm based on Bernstein polynomials for solving nonlinear fractional diffusion-wave equation. (English) Zbl 1427.65283

Summary: In this paper, a simple numerical algorithm based on Bernstein polynomials is presented and analyzed for obtaining numerical solution of nonlinear time fractional diffusion and wave-diffusion problems. The method is essentially based on reducing the differential equations with their initial and boundary conditions to a system of algebraic equations in the expansion coefficients of the sought for solutions. The equations are solved by collocation method. Two numerical examples are considered to ascertain the validity, wide applicability and efficiency of the proposed method. The obtained numerical results are compared with those obtained from known analytical solutions and are found to be very accurate and better than those obtained by others employing different techniques.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
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