【摘要】 带弱奇异核的偏积分微分方程能够表征记忆材料等新材料的机理和特性。采用Crank-Nicolson/sinc组合方法,利用Crank-Nicolson方法的高收敛精度,结合sinc配置方法的指数收敛,在时间方向采用Crank-Nicolson方法,在空间方向采用sinc配置方法,对带弱奇异核的偏积分微分方程进行离散,得到全离散格式,进而推导出相应的矩阵形式。全离散格式在时间方向上能达到1.5阶收敛,相比欧拉方法高0.5阶;在空间方向上也能达到比线性收敛更快速的收敛速度。Crank-Nicolson/sinc组合方法可推广到分数阶偏微分方程等更加复杂的方程的求解,以推动记忆类新材料等研发技术探索。更多还原

【Abstract】 Partial integro-differential equation with a weakly singular kernel can characterize the mechanism and properties of new materials such as memory materials.A joint Crank-Nicolson/sinc method is adopted,where the high convergence accuracy of Crank-Nicolson method is used,and by combining the exponential convergence of sinc collocation method,the Crank-Nicolson method is used in the time direction,and the sinc collocation method is used in the spatial direction,as to discretize the partial integro-differential equation with a weak singular kernel.The fully discrete scheme is obtained and the corresponding matrix form is derived.The full discrete scheme can achieve 1.5-order convergence in the time direction,0.5-order higher than the Euler method,and with a faster convergence speed than linear convergence in the space direction.The joint Crank-Nicolson/sinc method can be extended to solve more complex equations such as fractional partial differential equations,so as to promote the exploration of developing technologies such as memory-type new materials.更多还原