Abstract
In this paper, the rational spectral method combined with the Laplace transform is proposed for solving Robin time-fractional partial differential equations. First, a time-fractional partial differential equation is transformed into an ordinary differential equation with frequency domain components by the Laplace transform. Then, the spatial derivatives are discretized by the rational spectral method, the linear equation with the parameter s is solved, and the approximation Ux,s is obtained. The approximate solution at any given time, which is the numerical inverse Laplace transform, is obtained by the modified Talbot algorithm. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.
Highlights
Because the fractional-order calculus operator has nonlocality, it is suitable for describing the material involving memory and heredity in real life, and many practical problems can be described by fractional-order differential equations [1, 2]
Several studies have been conducted on the construction of approximate solutions for various fractional partial differential equations
The purpose of this article is to investigate a rational spectral method combined with the Laplace transform, to find approximate solutions for certain classes of Robin time-fractional PDEs with parameters that have derivatives in the sense of Caputo fractional derivatives as follows: C 0
Summary
Because the fractional-order calculus operator has nonlocality, it is suitable for describing the material involving memory and heredity in real life, and many practical problems can be described by fractional-order differential equations [1, 2]. Developing analytical and numerical methods for solving fractional PDEs is a very important task [3] To solve such problems, we need to introduce special functions to express the exact solutions of fractional differential equations, which can be very difficult. The purpose of this article is to investigate a rational spectral method combined with the Laplace transform, to find approximate solutions for certain classes of Robin time-fractional PDEs with parameters that have derivatives in the sense of Caputo fractional derivatives as follows:. Uðx, 0Þ = φðxÞ, uð0, tÞ + a∂xuð0, tÞ = v1ðtÞ, uðL, tÞ + b∂xuðL, tÞ = v2ðtÞ, ð2Þ where 0 < α ≤ 1, a, b ∈ R − f0g, and f , p, q are continuous real-valued functions This method results in an accurate solution that is continuous in the temporal domain and is computationally efficient.
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