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<p>In order to improve the spatial accuracy, this paper introduces the exponential integrator Fourier Galerkin method (EIFG) for solving semilinear parabolic equations in rectangular domains. The spatial discretization is first carried out by the Fourier-based Galerkin approximation, and then the time integration of the resulting semi-discrete system is approximated by the explicit exponential Runge-Kutta approach, giving rise to the fully-discrete numerical solution. With certain regularity assumptions on the model problem, error estimate measured in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-norm is explicitly derived for this method with two RK stages. Several two and three dimensional examples are shown to demonstrate the excellent performance of EIFG method, which verifies the theoretical results.</p>

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Exponential Integrator Fourier Galerkin Method for Semilinear Parabolic Equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月17日

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  • Jianguo Huang,
  • Lili Ju,
  • Yuejin Xu

摘要

In order to improve the spatial accuracy, this paper introduces the exponential integrator Fourier Galerkin method (EIFG) for solving semilinear parabolic equations in rectangular domains. The spatial discretization is first carried out by the Fourier-based Galerkin approximation, and then the time integration of the resulting semi-discrete system is approximated by the explicit exponential Runge-Kutta approach, giving rise to the fully-discrete numerical solution. With certain regularity assumptions on the model problem, error estimate measured in \(H^2\) H 2 -norm is explicitly derived for this method with two RK stages. Several two and three dimensional examples are shown to demonstrate the excellent performance of EIFG method, which verifies the theoretical results.