2024 : 11 : 13
Asghar Rahimi

Asghar Rahimi

Academic rank: Professor
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Education: PhD.
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Faculty: 1
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Research

Title
A new approach of B-spline wavelets to solve fractional differential equations
Type
JournalPaper
Keywords
B-spline wavelets Operational matrix of fractional derivative Multi–order fractional ordinary and partial differential equations Thresholding Error bounds and convergence Sparsity
Year
2024
Journal Communications in Nonlinear Science and Numerical Simulation
DOI
Researchers Abdolah Elahi ، Safar Irandoust Pakchin ، Asghar Rahimi ، Somaiyeh Abdi-mazraeh

Abstract

This paper presents a groundbreaking method for solving the multi-order fractional differential (M-OFD), both linear and nonlinear, as well as fractional partial differential equations (FPDE)s. This approach involves constructing an operational matrix of fractional derivatives using linear B-spline (LB-S) wavelet functions with perfect subtlety. The new method has two crucial features. Firstly, it simplifies the problem by converting it into a set of algebraic equations, which is a significant advantage. This makes the method highly accurate and reliable. Secondly, it uses thresholding to dramatically reduce the computational workload in linear problems. This leads to lightning-fast and highly efficient problem-solving. The newly developed scheme underwent a thorough examination of its error estimates and convergence, revealing remarkable results in terms of accuracy and efficiency. The analysis provides a comprehensive understanding of the scheme’s performance, highlighting its potential as a dependable and effective method. Based on the findings, it is evident that the proposed method not only delivers exceptional precision but also operates with remarkable efficiency.