# Solving Ordinary Differential Equation Using Least Square Method and Conjugate Gradient Method

### Abstract

This study all about to solve the problem of nonhomogeneous Ordinary differential equation with boundary value theorem (BVP). Because it is commonly appeared in range of field and profession such as engineering and physics. The theoretical method used to solve this problem is undetermined coefficient. Besides, this theoretical method is really complicated to understand and it will take a long time to solve the problems. Then this study proceeds to solve the problems using the numerical methods which are the Least Square Method (LSM) and another method is Conjugate Gradient (CG). CG is used to solve the inverse matrix to avoid ill-conditioned matrix. Numerical solution will show that Least Square Method can solved second-order nonhomogeneous ordinary differential equation with BVP based on term of the error analysis made by theoretical method which is undetermined coefficient. Finally, this study shows that the theoretical method and numerical methods almost lie in the same line when the solutions plotted on the same graph.

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**Mathematical Sciences and Informatics Journal**, [S.l.], v. 3, n. 2, p. 93-100, nov. 2022. ISSN 2735-0703. Available at: <https://myjms.mohe.gov.my/index.php/mij/article/view/17738>. Date accessed: 07 dec. 2022. doi: https://doi.org/10.24191/mij.v3i2.17738.