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Hussain, Manzoor; Haq, Sirajul; Ghafoor, Abdul; Ali, Ihteram

Numerical solutions of time-fractional coupled viscous Burgers’ equations using meshfree spectral method. (English) Zbl 1449.65273

Comput. Appl. Math. 39, No. 1, Paper No. 6, 21 p. (2020).
Summary: In this article, we compute numerical solutions of time-fractional coupled viscous Burgers’ equations using meshfree spectral method. Radial basis functions (RBFs) and spectral collocation approach are used for approximation of the spatial part. Temporal fractional part is approximated via finite differences and quadrature rule. Approximation quality and efficiency of the method are assessed using discrete \(E_2, E_{\infty }\) and \(E_{\text{rms}}\) error norms. Varying the number of nodal points \(M\) and time step-size \(\Delta t\), convergence in space and time is numerically studied. The stability of the current method is also discussed, which is an important part of this paper.

Cited in 8 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs

Keywords:

coupled Burgers’ equations; meshfree spectral method; radial basis functions; Caputo fractional derivative; shape parameter

Software:

Matlab
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Full Text: DOI

References:

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