General linear methods for Volterra integral equations

General linear methods for Volterra integral equations

s of IWANASP, September 10 – 12, 2008, Ericeira, Portugal GENERAL LINEAR METHODS FOR VOLTERRA INTEGRAL EQUATIONS ZDZISÃlAW JACKIEWICZ Departament of Mathematics, Arizona State University Tempe, Arizona 85287, USA E-mail: [email protected] We investigate the class of general linear methods of order p and stage order q = p for the numerical solution of Volterra integral equations of the se...

Linear Multistep Methods for Volterra Integral and Integro-Differential Equations

In these appendices we present, successively, I conditions for the existence of a unique solution of (1.1) and (1.2); II three tables of coefficients of forward differentiation formulas, and of two common LM formulas for ODEs, viz., backward differentiation formulas and Adams-Moulton formulas; III two lemmas which are needed in: IV proofs of the main results of this paper, as far as they are no...

General Linear Methods for Volterra Integro-differential Equations with Memory

A new class of numerical methods for Volterra integro-differential equations with memory is developed. The methods are based on the combination of general linear methods with compound quadrature rules. Sufficient conditions that guarantee global and asymptotic stability of the solution of the differential equation and its numerical approximation are established. Numerical examples illustrate th...

Approximate Solution of Linear Volterra-Fredholm Integral Equations and Systems of Volterra-Fredholm Integral Equations Using Taylor Expansion Method

In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equ...

Numerical method for non-linear fuzzy Volterra integral equations of the second kind