A Simple Introduction to the SM’s Method

Sanaullah Mastoi; Nabi Bux Kalhoro; Ali Bakhsh Mmugheri; Saeed Ahmed Rajput; Wan Ainun Mior Othman; Kumaresan Nallasamy

Author(s)

Sanaullah Mastoi Department of Basic Science and Related Studies, Quaid E Awam University of Engineering,Science and Technology (Campus) Larkana, (77150) Sindh,Pakistan

Nabi Bux Kalhoro Department of Basic Science and Related Studies, Quaid E Awam University of Engineering,Science and Technology (Campus) Larkana, (77150) Sindh,Pakistan

Ali Bakhsh Mmugheri Department of Basic Science and Related Studies, Quaid E Awam University of Engineering,Science and Technology (Campus) Larkana, (77150) Sindh,Pakistan

Saeed Ahmed Rajput Department of Basic Science and Related Studies, Quaid E Awam University of Engineering,Science and Technology (Campus) Larkana, (77150) Sindh,Pakistan

Wan Ainun Mior Othman Institute of Mathematical Science, Faculty of Science, University of Malaya, Kuala Lumpur (50603) Malaysia

Kumaresan Nallasamy Institute of Mathematical Science, Faculty of Science, University of Malaya, Kuala Lumpur (50603) Malaysia

Abstract

SM's Method is an iterative, random step size method, which is focused on the approximate solution. This method is also called as numerical or approximate method. The SM's method is abbreviated from the word Sanaullah Mastoi's Method. The method follows the numerical solution of partial differential equations through the finite-difference method. FD method is based on “grids” or “meshes”. The SM's method clearly explained the “Step size” or “Mesh size” or “Grid size”, with a specific rule which is randomly generated grids. In this method, the Mesh generation process can be followed through Mathematical programing, or the codes called as matrix laboratory or MATLAB. In this computing platform, the MATLAB 'nrand' commands are used for the random step size. The process of mesh generation does not define or found in any specific formula or principle. The idea or method helps the numerical solutions converging, rapid in solutions with the less computational time and error.

Publication Details

Page(s) 41-56

DOI DOI not available

Published Journal: The Sciencetech, Volume: 3, Issue: 2, Year: 2022

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Keywords

Fractional partial differential equations., SM’s Method, Finite difference method

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