In this study, we analyze the performance of a numerical scheme based on 3-scale Haar wavelets for dynamic Euler-Bernoulli equation, which is fourth order time dependent partial differential equation. This type equations governs behaviour vibrating beam and have many applications in elasticity. For its solution, first rewrite equation as system by introducing new variable, then use finite diffe...

‎the main purpose of this paper is to study the numerical solution of nonlinear volterra integral equations with constant delays, based on the multistep collocation method. these methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. also, we analyze the convergence of the...

This work, Bernoulli wavelet method is formed to solve nonlinear fuzzy Volterra-Fredholm integral equations. wavelets have been created by dilation and translation of polynomials. First we introduce properties polynomials, then used it transform the equations system algebraic We compared result proposed with exact solution show convergence advantages new method. The results got present are that...

The principal aim of this paper is to serve the numerical solution of an integralalgebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when t...

and Applied Analysis 3 Remark 5 (complex partial differential operators). Thepartial differential operators ∂/∂x and ∂/∂y are applied to a complexvalued function f = u + iV in the natural way: ∂f ∂x = ∂u ∂x + i ∂V ∂x , ∂f ∂y = ∂u ∂y + i ∂V ∂y . (7) We define the complex partial differential operators ∂/∂z and ∂/∂z by ∂ ∂z = 1 2 ( ∂ ∂x − i ∂ ∂y ) , ∂ ∂z = 1 2 ( ∂ ∂x + i ∂ ∂y ) . (8) Thus, ∂/∂x =...

The boundary knot method (BKM) is a recent meshfree boundary-type radial basis function (RBF) collocation technique. Compared with the method of fundamental solution, the BKM uses the nonsingular general solution instead of the singular fundamental solution to evaluate the homogeneous solution, while as such the dual reciprocity method (DRM) is still employed to approximate the particular solut...