The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.
This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.
The aim of this article was employed a fractional-shifted Legendre polynomials (F-SLPs) in a matrix form to approximate the temporal and spatial derivatives of fractional orders for derived an approximate solutions for bioheat problem of a space-time fractional. The spatial-temporal fractional derivatives are described in the formula by the Riesz-Feller and the Caputo fractional derivatives of orders v (1,2] and γ (0,1], respectively. The proposed methodology applied for two examples for demonstrating its usefulness and effectiveness. The numerical results confirmed that the utilized technique is immensely effective, provides high accuracy and good convergence.
Aims of this paper are to improve ADI differential quadrature method (ADI-DQM) based on Bernstein polynomials and add a new application to the differential quadrature method. By using the new methodology, the numerical solutions of the governing equations of unsteady two-dimensional flow of a polytropic gas are investigated. The numerical results reveal that the new technique is very effective and gives high accuracy, good convergence and reasonable stability.
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