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<p>In this paper, an element-free Galerkin method (EFGM) is proposed to solve the Sobolev equation with Burgers’ type nonlinearity. An explicit linearized temporal discretization scheme is employed to handle the nonlinear terms, ensuring second-order convergence accuracy in the temporal direction. Subsequently, a system of discrete linear algebraic equations is obtained by applying the EFGM. The stability of the linear time-discrete system is analyzed, and the theoretical error analysis of the EFGM for the Sobolev equation is conducted. Numerical experiments validate the effectiveness of the method and the theoretical analysis. Numerical results demonstrate that the EFGM surpasses some existing methods in both accuracy and convergence order, highlighting its advantages of high precision and efficiency.</p>

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Numerical analysis of the Sobolev equation with Burgers’ type nonlinearity by an element-free Galerkin method

  • 期刊论文

  • 发表日期：

    2026年2月20日

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  • Yikang Wang,
  • Zesen Hu,
  • Xiaolin Li

摘要

In this paper, an element-free Galerkin method (EFGM) is proposed to solve the Sobolev equation with Burgers’ type nonlinearity. An explicit linearized temporal discretization scheme is employed to handle the nonlinear terms, ensuring second-order convergence accuracy in the temporal direction. Subsequently, a system of discrete linear algebraic equations is obtained by applying the EFGM. The stability of the linear time-discrete system is analyzed, and the theoretical error analysis of the EFGM for the Sobolev equation is conducted. Numerical experiments validate the effectiveness of the method and the theoretical analysis. Numerical results demonstrate that the EFGM surpasses some existing methods in both accuracy and convergence order, highlighting its advantages of high precision and efficiency.