延迟双曲方程的Crank-Nicolson有限差分方法研究

Research on Crank-Nicolson finite difference method for fractional delay hyperbolic equations

延迟偏微分方程是一种既依赖于当前状态又依赖于过去状态的过程系统,能客观准确地解释很多自然现象的规律。为解决延迟难以获得精确解的问题,构建延迟微分方程数值求解方法。对延迟双曲方程构造Crank-Nicolson差分格式,并借助非线性和线性延迟双曲方程的数值算例,验证了Crank-Nicolson有限差分方法的有效性。

Delayed partial differential equation is a kind of process system which depends on both the current state and the past state.It can explain many laws of natural phenomena objectively and accurately.In order to solve the problem that it is difficult to obtain accurate solution due to the influence of delay,a numerical solution method for delay differential equation is constructed.A Crank-Nicolson difference scheme was constructed for the delayed hyperbolic equation,and the effectiveness of the Crank-Nicolson finite difference method was verified by numerical examples of nonlinear and linear delayed hyperbolic equations.