Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. An example is provided to illustrated the applicability of the method.

The computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...

in this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. the sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. then, the newton-raphson method is used for solving these sets of algebraic equations. to present ability ...

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon ex...

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

We reduce the two phase Stefan problem with kinetic to a system of nonlinear Volterra integral equations of second kind and apply Newton's method to linearize it. We found product integration solution of the linear form. Sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.

in this paper, we propose and analyze an efficient matrix methodbased on bell polynomials for numerically solving nonlinear fredholm- volterraintegral equations. for this aim, first we calculate operational matrix of integration and product based on bell polynomials. by using these matrices, nonlinearfredholm-volterra integral equations reduce to the system of nonlinear algebraicequations which...

‎In this paper‎, ‎we study the numerical solution of Convection-Diffusion equation with a memory term subject to initial boundary value conditions‎. ‎Finite difference method in combination with product trapezoidal integration rule is used to discretize the equation in time and sinc collocation method is employed in space‎. ‎The accuracy and error analysis of the method are discussed‎. ‎Numeric...