This paper explains and applies a numerical technique utilizing the cubicb-spline functions and the mean value theorem (MVT) to solve a general time fractional partial differential equation (FPDE). The MVT for integr...
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In this paper, a numerical method is proposed to approximate the solution of the nonlinear parabolic partial differential equation with Neumann's boundary conditions. The method is based on collocation of cubicb-...
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In this paper, a numerical method is proposed to approximate the solution of the nonlinear parabolic partial differential equation with Neumann's boundary conditions. The method is based on collocation of cubicb-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubicb-splines for spatial variable and its derivatives, which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK3 scheme. The numerical approximate solutions to the nonlinear parabolic partial differential equations have been computed without transforming the equation and without using the linearization. Four illustrative examples are included to demonstrate the validity and applicability of the technique. In numerical test problems, the performance of this method is shown by computing L-infinity and L-2 error norms for different time levels. Results shown by this method are found to be in good agreement with the known exact solutions. (C) 2012 Elsevier b. V. All rights reserved.
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