Gao, J.; He, S.; Bai, Q.; Liu, J. A Time Two-Mesh Finite Difference Numerical Scheme for the Symmetric Regularized Long Wave Equation. Fractal Fract.2023, 7, 487.
Gao, J.; He, S.; Bai, Q.; Liu, J. A Time Two-Mesh Finite Difference Numerical Scheme for the Symmetric Regularized Long Wave Equation. Fractal Fract. 2023, 7, 487.
Gao, J.; He, S.; Bai, Q.; Liu, J. A Time Two-Mesh Finite Difference Numerical Scheme for the Symmetric Regularized Long Wave Equation. Fractal Fract.2023, 7, 487.
Gao, J.; He, S.; Bai, Q.; Liu, J. A Time Two-Mesh Finite Difference Numerical Scheme for the Symmetric Regularized Long Wave Equation. Fractal Fract. 2023, 7, 487.
Abstract
This paper proposed a time two-mesh (TT-M) finite difference numerical scheme to improve the efficiency of solving the symmetric regularized long wave (SRLW) equation. The TT-M Crank-Nicolson discretization and finite difference method are employed in time and space approximation respectively. The scheme involves three main steps: firstly, the time interval is divided into coarse and fine time meshes, then the nonlinear system is solved on the coarse time mesh; secondly, coarse numerical solutions on the fine time mesh are computed using an interpolation formula based on the solutions derived in the step one; lastly, the TT-M finite difference numerical solutions can be obtained through constructing the linearized fine time mesh system using Taylor’s formula. Compared to the currently existing TT-M numerical methods, the novelty of this study is that the nonlinear term including derivatives is linearized by Taylor’s formula for a function with three variables, whose error analysis is more complex. Finally, some numerical examples, including computational time and accuracy, preservation of conservation laws, are given to verify the efficiency of the scheme. By comparing it with the standard nonlinear finite difference scheme, this method can reduce CPU time without sacrificing accuracy.
Keywords
SRLW equation; finite difference; time two-mesh; convergence analysis; conservation law
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright:
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