In this article, a numerical method based on  improvement of block-pulse functions (IBPFs) is discussed for solving the system of linear Volterra and Fredholm integral equations. By using IBPFs and their operational matrix of integration, such systems can be reduced to a linear system of algebraic equations. An efficient error estimation and associated theorems for the proposed method are also ...

‎In this paper‎, ‎an efficient algorithm for solving a system of linear‎ ‎equations based on the homotopy analysis method is presented‎. ‎The‎ ‎proposed method is compared with the classical Jacobi iterative‎ ‎method‎, ‎and the convergence analysis is discussed‎. ‎Finally‎, ‎two‎ ‎numerical examples are presented to show the effectiveness of the‎ ‎proposed method.‎

We illustrate several adaptive algorithms for the solutions of bi-infinite singular linear systems. Such algorithms are realized from exact iterative schemes (e.g., Richardson, steepest-descent methods, matching pursuit) by finite dimensional approximations of each iteration, performed with a greedy approach. We show that these algorithms are convergent and optimal with respect to certain spars...

The paper illustrates the use of a symbolic software package GeM for Maple to compute local symmetries of nonlinear and linear differential equations (DE). In the cases when a given DE system contains arbitrary functions or parameters, symbolic symmetry classification is performed. Special attention is devoted to the computation of point symmetries of linear PDE systems. Routines are available ...

In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridi...

A system of homogeneous linear equations with integer coefficients is partition regular if, whenever the natural numbers are finitely coloured, the system has a monochromatic solution. The Finite Sums theorem provided the first example of an infinite partition regular system of equations. Since then, other such systems of equations have been found, but each can be viewed as a modification of th...

Entropy generation in an unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel plates in a rotating system have been analyzed. Both the lower and upper plates of the channel are subjected to asymmetric convective heat exchange with the ambient following the Newton's law of cooling. A numerical solution for governin...