A novel adaptive meshless method for solving the nonlinear time fractional telegraph equations on arbitrary domains

A novel adaptive meshless numerical method for tackling with the two-dimensional time fractional telegraph equations on arbitrary domains based on partitioning domains is presented in this paper. The proposed approach has many advantages. (i) When the exact solution varies dramatically in some parts of the domain and gently in others, our method can reduce the amount of calculation waste and improve computational speed. (ii) With the assistance of the extension theorem, the multiscale orthonormal bases of two-dimensional reproducing kernel space on rectangle regions are constructed to obtain the approximate solutions of the equations on arbitrary domains, which can achieve high accuracy. (iii) The convergence-order analysis of bicubic spline space can be employed to study the convergence order of the proposed strategy primely. Eventually, some numerical examples and comparisons graphically elucidate the implementation and capability of the adaptive meshless method, which is more accurate and efficient than some existing methods.