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ABSTRACT <p>Two-dimensional multi-term time-space fractional diffusion-wave equations are considered. An alternating direction implicit (ADI) spectral method is developed based on Legendre spectral approximation in space and finite difference discretization in time. We also prove the numerical stability and convergence of the developed scheme and that the error is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O(\tau^2 + N^{\gamma - r})\)</EquationSource> <EquationSource Format="MATHML"><math display="inline"> <mrow> <mi>O</mi> <mo>(</mo> <msup> <mi>τ</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>N</mi> <mrow> <mi>γ</mi> <mo>−</mo> <mi>r</mi> </mrow> </msup> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(N, \tau, \gamma, r\)</EquationSource> <EquationSource Format="MATHML"><math display="inline"> <mrow> <mi>N</mi> <mo>,</mo> <mi>τ</mi> <mo>,</mo> <mi>γ</mi> <mo>,</mo> <mi>r</mi> </mrow> </math></EquationSource> </InlineEquation> are the polynomial degree, time step size, Riesz derivative order, and the regularity of the exact solution, respectively.</p>

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An Alternating Direction Implicit Spectral Method for Two-Dimensional Multi-Term Time-Space Fractional Diffusion-Wave Equations

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Yong-Suk Kang,
  • Chu-Myong Ri,
  • Chol-Guk Choe

摘要

ABSTRACT

Two-dimensional multi-term time-space fractional diffusion-wave equations are considered. An alternating direction implicit (ADI) spectral method is developed based on Legendre spectral approximation in space and finite difference discretization in time. We also prove the numerical stability and convergence of the developed scheme and that the error is \(O(\tau^2 + N^{\gamma - r})\) O ( τ 2 + N γ − r ) , where \(N, \tau, \gamma, r\) N , τ , γ , r are the polynomial degree, time step size, Riesz derivative order, and the regularity of the exact solution, respectively.