Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix

2021 ◽  
Vol 161 ◽  
pp. 244-274
Author(s):  
Nikhil Srivastava ◽  
Aman Singh ◽  
Yashveer Kumar ◽  
Vineet Kumar Singh
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Operational Matrix ◽  
Numerical Algorithms ◽  
Riesz Space ◽  
Fractional Partial Differential Equations ◽  
Partial Differential

The Coupling of RBF and FDM for Solving Higher Order Fractional Partial Differential Equations

2014 ◽  
Vol 598 ◽  
pp. 409-413 ◽  
Author(s):  
Zakieh Avazzadeh ◽  
Wen Chen ◽  
Vahid Reza Hosseini
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Discrete Solution ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Time Direction ◽  
Radial Basis

In this work, we describe the radial basis functions for solving the time fractional partial differential equations defined by Caputo sense. These problems can be discretized in the time direction based on finite difference scheme and is continuously approximated by using the radial basis functions in the space direction which achieves the semi-discrete solution. Numerical results accuracy the efficiency of the presented method.

scholarly journals Technique to Solve Linear Fractional Differential Equations Using B-Polynomials Bases

2021 ◽  
Vol 5 (4) ◽  
pp. 208
Author(s):  
Muhammad I. Bhatti ◽  
Md. Habibur Rahman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Fractional Order ◽  
Initial Conditions ◽  
Operational Matrix ◽  
Basis Sets ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
The Galerkin Method

A multidimensional, modified, fractional-order B-polys technique was implemented for finding solutions of linear fractional-order partial differential equations. To calculate the results of the linear Fractional Partial Differential Equations (FPDE), the sum of the product of fractional B-polys and the coefficients was employed. Moreover, minimization of error in the coefficients was found by employing the Galerkin method. Before the Galerkin method was applied, the linear FPDE was transformed into an operational matrix equation that was inverted to provide the values of the unknown coefficients in the approximate solution. A valid multidimensional solution was determined when an appropriate number of basis sets and fractional-order of B-polys were chosen. In addition, initial conditions were applied to the operational matrix to seek proper solutions in multidimensions. The technique was applied to four examples of linear FPDEs and the agreements between exact and approximate solutions were found to be excellent. The current technique can be expanded to find multidimensional fractional partial differential equations in other areas, such as physics and engineering fields.

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