Solution for Second-Order Differential Equation Using Least Square Method

Abstract

This paper studies the numerical method for solving differential equations. The continuous least square method (CLSM) is used to obtain the explicit solution for solving ordinary differential equations (ODEs), partial differential equations (PDEs), and fractional differential equations (FDEs), but in this work, we consider the explicit results from CLSM approach and applied it on second-order ODEs. Moreover, the L_2 norm is used to obtain the minimum approximation error. The numerical results obtained has a good agreement with the exact solution with minimum approximation error. The explicit results are supported by an example that was treated with Matlab and Matematica 11.

Keywords

• differential equation
• second-order differential equation
• continuous least square method
• and l_2 norm