基于RK-LS-SVM求常微分方程的近似解  

Approximate Solution of Ordinary Differential Equations Based on RK-LS-SVM

作　　者：胡蝶 吴俊 肖海霞[1] 黄尚柱 Hu Die;Wu Jun;Xiao Haixia;Huang Shangzhu(School of Mathematics,Physics&Optoelectronic Engineering,Hubei University of Automotive Technology,Shiyan 442002,China)

机构地区：[1]湖北汽车工业学院数理与光电工程学院,湖北十堰442002

出　　处：《湖北汽车工业学院学报》2025年第1期20-22,27,共4页Journal of Hubei University Of Automotive Technology

基　　金：应用数学湖北省重点实验室开放基金(HBAM202105)。

摘　　要：针对线性常微分方程的初值问题,提出一种将Runge-Kutta法与最小二乘支持向量机(LS-SVM)相结合的RK-LS-SVM方法求近似解。首先通过4阶Runge-Kutta法求出微分方程的数值解,然后将此数值解转化为LSSVM回归模型的约束条件,进而求解优化问题,所得闭式近似解连续可微,精度较高。数值算例验证了RK-LSSVM方法的有效性和可行性。A RK-LS-SVM method combining the Runge-Kutta(RK) method with the least squares support vector machine(LS-SVM) was proposed to approximate the initial value problem of linear ordinary differential equations.Firstly,the numerical solution of the differential equation was obtained through the fourth-order Runge-Kutta method.Then,this numerical solution was transformed into the constraint conditions of the LS-SVM regression model,and the optimization problem was solved.The obtained approximate solution in closed form was continuously differentiable with high accuracy.Numerical examples have verified the effectiveness and feasibility of this method.

关 键 词：RUNGE-KUTTA法 LS-SVM 线性常微分方程 初值问题 

分 类 号：O241.81[理学—计算数学]