Fractional differential quadrature techniques for fractional order Cauchy reaction-diffusion equations. (English) Zbl 1530.65134
Summary: This paper aims to explore and apply differential quadrature based on different test functions to find an efficient numerical solution of fractional order Cauchy reaction-diffusion equations (CRDEs). The governing system is discretized through time and space via novel techniques of differential quadrature method and the fractional operator of Caputo kind. Two problems are offered to explain the accuracy of the numerical algorithms. To verify the reliability, accuracy, efficiency, and speed of these methods, computed results are compared numerically and graphically with the exact and semi-exact solutions. Then mainly, we deal with absolute errors and \(L_\infty\) errors to study the convergence of the presented methods. For each technique, MATLAB Code is designed to solve these problems with the error reaching \(\leq1 \times 10^{-5}\). In addition, a parametric analysis is presented to discuss influence of fractional order derivative on results. The achieved solutions prove the viability of the presented methods and demonstrate that these methods are easy to implement, effective, highly accurate, and appropriate for studying fractional partial differential equations emerging in fields related to science and engineering.
{© 2023 John Wiley & Sons Ltd.}
{© 2023 John Wiley & Sons Ltd.}
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35K57 | Reaction-diffusion equations |
| 35R11 | Fractional partial differential equations |
Keywords:
Caputo; Cauchy reaction-diffusion equation; discrete singular convolution; fractional order derivatives; quadrature methods; statistical analysisReferences:
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