Numerical solution of DAE systems using block BDF methods

Numerical solution of linear control systems using interpolation scaling functions

The current paper proposes a technique for the numerical solution of linear control systems.The method is based on Galerkin method, which uses the interpolating scaling functions. For a highly accurate connection between functions and their derivatives, an operational matrix for the derivatives is established to reduce the problem to a set of algebraic equations. Several test problems are given...

Numerical Solution of Sawada-Kotera equation by using Iterative Methods

Numerical solution of nonlinear integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions

In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of...

Solving Differential Riccati Equations Using BDF Methods

This technical report describes three approaches for solving the Differential Riccati Equation (DRE), by means of the Backward Differentiation Formula (BDF) and resolution of the corresponding implicit equation, using Newton's method. These approaches are based on: GMRES method, resolution of Sylvester equation and fixed point method. The role and use of DRE is especially important in optimal c...

The Parallel Solution of Almost Block Diagonal Systems Arising in Numerical Methods for BVPs for ODEs

Three parallel algorithms are presented for solving the Almost Block Diagonal (ABD) systems of linear algebraic equations that arise during the numerical solution of Boundary Value Problems (BVPs) for Ordinary Differential Equations (ODEs). Until recently, the solution of these systems has proven to be the execution-time bottleneck in the parallel implementation of most BVP codes. Several numer...