in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

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In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

‎‎‎in this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear volterra integral equations (2d-nvies) of the first kind‎. ‎here‎, ‎we convert a 2d-nvie of the first kind to a one-dimensional linear vie of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎we also verify convergence and error analysis of the method‎. ‎at t...

as an application of hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. we have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear backlund transformations and construction of ...

The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is...

this work reports the results of the application of the second-order maccormack method for numerical solution of‎ the conservative form of two-dimensional non-hydrostatic and fully compressible navier-stokes equations governing an inviscid and adiabatic atmosphere‎. various aspects of the computational approach such as discretization of the governing equations for the interior and boundary poin...

a two-dimensional single particle finite element model was used to examine the effects of particle fragmental pattern on the average molecular weights, polymerization rate and particle overheating in heterogeneous ziegler-natta olefin polymerization. a two-site catalyst kinetic mechanism was employed together with a dynamic two-dimensional molecular species in diffusion-reaction equation. the i...