Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficients - Amin Rohul; Nawaz Muhammad; Shah Kamal; Abdeljawad Thabet (Nonlinear Engineering)
In this article, Haar wavelet collocation method is applied for the solution of fourth-order integro-differential equations. Also, a fixed point approach is used to investigate the existence theory of solution to the considered problem. The fourth-order derivative is approximated using Haar function. In addition, third-, second-, and first-order derivatives together with unknown functions are obtained by the process of successive integrations. On applying the Haar collocation method, the suggested problem of IDEs is transformed to a system of algebraic equations. The Gauss elimination scheme is used for the solution of linear algebraic equations. The precision, effectiveness, and convergence of the Haar approach are checked on some test problems. Different collocation and Gauss points are used to determine the absolute and root mean square errors. To demonstrate the applicability of the proposed method, an experimental rate of convergence is calculated, which is almost equal to 2. The method is accurate, easily applicable, and efficient.