a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framewo...

‎In this article‎, we use a finite difference technique‎ ‎to solve variable-order fractional integro-differential equations‎ ‎(VOFIDEs‎, ‎for short)‎. ‎In these equations‎, ‎the variable-order fractional integration(VOFI) and‎ ‎variable-order fractional derivative (VOFD) are described in the‎ ‎Riemann-Liouville's and Caputo's sense,respectively‎. ‎Numerical experiments‎, ‎consisting of two exam...

In order to obtain a solution to an optimal control problem‎, ‎a numerical technique based on state-control parameterization method is presented‎. ‎This method can be facilitated by the computation of performance index and state equation via approximating the control and state variable as a function of time‎. ‎Several numerical examples are presented to confirm the analytical findings and illus...

This paper is intended to provide a numerical algorithm based on random sampling for solving the linear Volterra integral equations of the second kind. This method is a Monte Carlo (MC) method based on the simulation of a continuous Markov chain. To illustrate the usefulness of this technique we apply it to a test problem. Numerical results are performed in order to show the efficiency and accu...

a fundamental topic in computational fluid dynamics is the role of coordinate particularly for searching optimized coordinates. the objective of this study is the numerical modeling of supersonic flows using a new coordinate system i.e. unified coordinate system (ucs) uses moving mesh with motionless viewing window technique. ucs has an advantage over traditional coordinate systems (eulerian an...

in this work, we present a computational method for solving second kindnonlinear fredholm volterra integral equations which is based on the use ofhaar wavelets. these functions together with the collocation method are thenutilized to reduce the fredholm volterra integral equations to the solution ofalgebraic equations. finally, we also give some numerical examples that showsvalidity and applica...

In this paper numerical technique has been used to solve multidimensional unsteady state heat conduction equation with Dirichlet boundary conditions. We focus on finite volume numerical technique for solution of multidimensional time dependent heat conduction problems. Finally, the efficiency of this technique is tested for some heat conduction problems with known analytical solutions and the n...