scholarly journals On a novel iterative method to compute polynomial approximations to Bessel functions of the first kind and its connection to the solution of fractional diffusion/diffusion-wave problems

2011 ◽  
Vol 44 (7) ◽  
pp. 075203
Author(s):  
Santos Bravo Yuste ◽  
Enrique Abad
Keyword(s):  
Iterative Method ◽  
Bessel Functions ◽  
Fractional Diffusion ◽  
Diffusion Wave ◽  
Polynomial Approximations ◽  
Wave Problems

Solution of fractional partial differential equations using iterative method

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
Chandradeepa Dhaigude ◽  
Vasant Nikam
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Method ◽  
Initial Value Problems ◽  
Wave Equations ◽  
Fractional Diffusion ◽  
Fractional Partial Differential Equations ◽  
Initial Value ◽  
Diffusion Wave ◽  
Linear And Nonlinear

AbstractThe purpose of this paper is to obtain solutions for both linear and nonlinear initial value problems (IVPs) for fractional transport equations and fractional diffusion-wave equations using the iterative method.

scholarly journals Approximate Solutions of Time Fractional Diffusion Wave Models

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 923 ◽  
Author(s):  
Abdul Ghafoor ◽  
Sirajul Haq ◽  
Manzoor Hussain ◽  
Poom Kumam ◽  
Muhammad Asif Jan
Keyword(s):  
Finite Difference ◽  
Wave Equations ◽  
Quadrature Rule ◽  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Haar Wavelets ◽  
Test Problems ◽  
Algebraic Equations ◽  
Diffusion Wave ◽  
Wave Models

In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing L 2 and L ∞ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before.

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