Solving nonlinear wave equations based on barycentric Lagrange interpolation. (English) Zbl 07906465
Summary: In this paper, we deeply study the high-precision barycentric Lagrange interpolation collocation method to solve nonlinear wave equations. Firstly, we introduce the barycentric Lagrange interpolation and provide the differential matrix. Secondly, we construct a direct linearization iteration scheme to solve nonlinear wave equations. Once again, we use the barycentric Lagrange interpolation to approximate the \((2+1)\) dimensional nonlinear wave equations and \((3+1)\) dimensional nonlinear wave equations, and describe the matrix format for direct linearization iteration of the nonlinear wave equations. Finally, the comparative experiments show that the barycentric Lagrange interpolation collocation method for solving nonlinear wave equations have higher calculation accuracy and convergence rate.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35L05 | Wave equation |
Keywords:
barycentric Lagrange interpolation; differential matrix; linearized iterative format; nonlinear wave equationReferences:
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