An improved method based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders

Application of Higher Order Haar Wavelet Method for Solving Nonlinear Evolution Equations

“…[42] as an improvement of the Haar wavelet method (HWM) originally introduced by Chen and Hsiao in [15]. The HWM has been proposed for solving differential equations [15,27,51] as well as a wide class of integro-differential and integral equations [5,7,8,14,35,37,63]. According to HWM, as proposed in [15,27], the highest order derivative included in the differential equation is expanded into the series of Haar functions.…”

Non-standard Volterra integral equations: a mean-value theorem numerical approach

“…The exact solution is √ 2 + x. The equation (14) is taken from [10] and solved numerically by Nedaiasl et al [12] by means of Runge-Kutta and barycentric rational quadrature types. It is easy to see that Proposition 2.1 is verified.…”

“…Moreover, Aziz et al [3] proposed a method based on Haar wavelet for the numerical solution of two-dimensional non-linear integral equations. Siraj-ul-Islam et al [14] suggested a novel technique based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders.…”

A new numerical method for a class of Volterra and Fredholm integral equations

“…Moreover, Aziz et al [2] proposed a method based on Haar wavelet for the numerical solution of two-dimensional non-linear integral equations. Siraj-ul-Islam et al [17] suggested a novel technique based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders.…”