As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numer...

We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave equations, such as Boussinesq-type equations, follow from the present model for...

In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.

Nonlinear cross-correlation equations in finite and semi-infinite intervals are studied by means of Fourier transform and Cauchy integral techniques. The equations are reduced to a bilinear conjugacy problem for two analytic functions on the real axis which can be solved in explicit form. In particular, Engibaryan’s equations from nonlinear factorization theory of Wiener-Hopf integral equations...

in this paper‎, ‎existence of an $l^p$-solution for 2dies (two‎ ‎dimensional integral equations) of the hammerstein type is‎ ‎discussed‎. ‎the main tools in this discussion are schaefer's and‎ ‎schauder's fixed point theorems with a general version of‎ ‎gronwall's inequality‎.