一个求解二维非线性时间分数阶波动方程的向后欧拉差分格式

A Backward Euler Difference Scheme for Solving Two-Dimensional Nonlinear Time Fractional Wave Equations

基于所考虑方程的等价积分-微分形式,将卷积求积公式与向后欧拉差分公式相结合,建立了一种求解二维非线性时间分数阶波动方程的数值格式.通过理论推导说明该格式在时空方向上的精度为O(τ+h^(2)_(1)+h^(2)_(2)),并用数值算例验证了该结论.

Based on the equivalent integral-differential form of the considered equation,this study combines the Convolution Quadrature Formula with the backward Euler Difference Scheme to establish a numerical scheme for solving two-dimensional nonlinear time fractional wave equations.The theoretical analysis demonstrates that the proposed scheme possesses a spatial-temporal accuracy of Numerical examples are provided to validate this conclusion.