Symplectic Radial Basis Approximation of Multi-variate Hamiltonian PDEs

Abstract

A meshless symplectic algorithm for multi-dimensional linear Hamiltonian partial differential equations with radial basis interpolation has been suggested when the solving domain is $${\mathbb {R}}^d$$ . In this study, for sake of application, the energy error estimate of the proposed symplectic scheme is made when the targeted domain is bounded. The paper also extends the algorithm to solve the nonlinear two-dimensional Klein–Gordon equation. As numerical experiments shown, the algorithm preserves the discretization energy, and it is efficient to deal with the nonlinear case.