利用带有改进算子矩阵的模块脉冲函数求非线性随机微分方程数值解  

Numerical Solution of Nonlinear Stochastic Differential Equations by Block Pulse Functions with Improved Operator Matrix

作　　者：姜国 刘富钢 陈丹 JIANG Guo;LIU Fugang;CHEN Dan(School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《应用数学》2023年第4期1059-1068,共10页Mathematica Applicata

基　　金：Supported by the NSF Grant of Hubei Province(2022CFD042,2023AFD013)。

摘　　要：本文介绍基于改进算子矩阵的模块脉冲函数求解非线性随机微分方程的有效数值方法.利用模块脉冲函数的积分算子矩阵将非线性随机积分方程转化为代数方程.此外,我们进行了误差分析,并证明该方法收敛更快.最后,通过数值算例对该方法进行了验证.This paper introduces an effective numerical method based on the block pulse functions with improved operator matrix to solve the nonlinear stochastic differential equations.The nonlinear stochastic differential equation is transformed into a set of algebraic equations by the improved operator matrix of block pulse function.Furthermore,we perform an error analysis and demonstrate that the method converges faster.Finally,numerical examples are used to support the method.

关 键 词：随机微分方程 改进算子矩阵 模块脉冲函数 

分 类 号：O211.6[理学—概率论与数理统计]