International Journal of Industrial Engineering & Production Research

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For numerical examples, the solutions may be produced with good accuracy, by choosing suitable trial and test spaces in Petrov-Galerkin method.

 Abstract : The meshless local Petrov-Galerkin method with unity as the weighting function has been applied to the solution of the Navier-Stokes and energy equations. The Navier-Stokes equations in terms of the stream function and vorticity formulation together with the energy equation are solved for a driven cavity flow for moderate Reynolds numbers using different point distributions. The L²-norm of the error as a function of the size of the control volumes is presented for different cases and the rate of convergence of the method is established. The results of this study show that the proposed method is applicable in solving a variety of non-isothermal fluid flow problems.