Identifying a Space-Dependent Source Term and the Initial Value in a Time Fractional Diffusion-Wave Equation

Lv, Xianli; Feng, Xiufang

doi:10.3390/math11061521

Cited by 1 publication

(2 citation statements)

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“…Equations ( 16) and ( 17) give the bounds for the constant δ. For system (14), the pseudoinverse may be hard to compute, but by using it, stability is guaranteed. The MATLAB condest function can be used for evaluating…”

Section: Stabilitymentioning

confidence: 99%

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A Hybrid Local Radial Basis Function Method for the Numerical Modeling of Mixed Diffusion and Wave-Diffusion Equations of Fractional Order Using Caputo’s Derivatives

et al. 2023

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This article presents an efficient method for the numerical modeling of time fractional mixed diffusion and wave-diffusion equations with two Caputo derivatives of order 0<α<1, and 1<β<2. The numerical method is based on the Laplace transform technique combined with local radial basis functions. The method consists of three main steps: (i) first, the Laplace transform is used to transform the given time fractional model into an equivalent time-independent inhomogeneous problem in the frequency domain; (ii) in the second step, the local radial basis functions method is utilized to obtain an approximate solution for the reduced problem; (iii) finally, the Stehfest method is employed to convert the obtained solution from the frequency domain back to the time domain. The use of the Laplace transform eliminates the need for classical time-stepping techniques, which often require very small time steps to achieve accuracy. Additionally, the application of local radial basis functions helps overcome issues related to ill-conditioning and sensitivity to shape parameters typically encountered in global radial basis function methods. To validate the efficiency and accuracy of the proposed method, several test problems in regular and irregular domains with uniform and non-uniform nodes are considered.

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Section: Stabilitymentioning

confidence: 99%

“…Wyss [11] obtained the solution of the fractional diffusion equation using Fox functions. Some notable works have been done on the theoretical analysis of FODEs (see [12][13][14] and references therein).…”

Section: Introductionmentioning

confidence: 99%