A new method based on Haar wavelet for the numerical solution of two-dimensional nonlinear integral equations

A new numerical method based on Haar wavelet is proposed for two-dimensional nonlinear Fredholm, Volterra and Volterra–Fredholm integral equations of first and second kind. The proposed method is an extension of the Haar wavelet method Aziz and Siraj-ul-Islam (2013), Siraj-ul-Islam et al. (2013) and Siraj-ul-Islam et al. (2014) from one-dimensional nonlinear integral equations (Fredholm and Volterra) to two-dimensional nonlinear integral equations (Fredholm, Volterra and Volterra–Fredholm). The main characteristic of the method is that, unlike several other methods, it does not involve numerical integration which results in an improved accuracy of the method. In order to show the effectiveness of the method, it is applied to several benchmark problems. The numerical results are compared with other methods existing in the recent literature.