A compact difference scheme for two-dimensional nonlinear time-fractional wave equations with initial singularity(求解具有初始奇异性的二维非线性时间分数阶波动方程的紧差分格式)

Abstract

Based on the equivalent integral-differential form of the equation considered, an alternate directional implicit (ADI) numerical scheme for two-dimensional nonlinear time-fractional wave equations with initial singularity was developed by combining the convolution quadrature formula with the Crank-Nicolson technique. Theoretical derivation shows that the scheme has at least order γ accuracy in time direction and order 4 accuracy in space direction. Finally, a numerical example is demonstrated to verify the conclusion.(基于具有初始奇异性的二维非线性时间分数阶波动方程的等价积分-微分形式，将卷积求积公式与Crank-Nicolson技术相结合，建立了求解该方程的交替方向隐式（alternate directional implicit，ADI）数值格式。理论推导说明，该格式在时间方向上至少具有γ阶精度，在空间方向上具有4阶精度，并用数值算例进行了验证。)

Keywords

• initial singularity(初始奇异性)
• time fractional order(时间分数阶)
• wave equation(波动方程)