Haar Wavelet for Numeric Solution of Rlc Circuit Differential Equations

Abstract

The wavelet transformation is a mathematical method developed over the past decades to be adapted for applications in the fields of science and engineering. The wavelet transform can be applied in the field of numerical analysis to solve the differential equation. This paper is concerned with applying Haar wavelet methods to solve an ordinary differential equation for an RLC series circuit with a known initial state. The matrix construction calculations are proposed in a simple way. Three numerical mathematical examples are shown that include second-order differential equations with variable and constant coefficients. The results showed that the proposed method is quite reasonable while comparing the solution of second order systems by Haar wavelet method with the exact solution in the context of serial RLC circuit. Moreover, the use of Haar waves is found to be simple, accurate, with flexible and appropriate arithmetic computational costs.