三元一阶线性非齐次微分方程组解法分析

Solution Analysis of First Order Linear Non-homogeneous Differential Equations with Three Variables

针对传统三元一阶线性非齐次微分方程组求解方法对特征解计算的精度较低,导致求解耗时较长、计算结果可靠性较差的问题,设计了新型三元一阶线性非齐次微分方程组求解方法.采用Matlab软件作为求解过程实施平台,根据方程组特征设定软件部件以及边值计算过程,完成方程组非齐次特征值求解,并分析非齐次特征值扰动性,获取高精度特征值的解;对三元一阶线性非齐次微分方程组进行变形转化,将非齐次特征值作为方程组求解过程的约束条件,结合传统解法完成方程组求解.结果表明:与传统解法对比,此解法的求解耗时较短,计算结果与已知结果相似度较高,计算结果具有一定的可靠性.使用此解法可有效提升对三元一阶线性非齐次微分方程组的计算能力.

In view of the low accuracy of the traditional three variable first-order linear non-homogeneous differential equations,which results in a long time-consuming solution and poor reliability of the calculation results,a new method for solving the first-order linear non-homogeneous differential equations with three variables is designed.Matlab software is used as the implementation platform of the solution process,and the software components and boundary values are set according to the characteristics of the equations.And the disturbance of the non-homogeneous eigenvalues is analyzed to obtain the solutions of high-precision eigenvalues.The three variables first-order linear non-homogeneous differential equations are transformed,taking the non-homogeneous eigenvalues as the constraints in the process of solving the equations and combined with the traditional solution,to solve the equations.The test results show that,compared with the traditional solution,this solution takes less time with higher accuracy and its calculated results are more similar to the known results.The calculated results have certain reliability.This method can effectively improve the computational ability of the system of three variables first-order linear non-homogeneous differential equations.