On Solvability Of The Integro-Differential Equations

On the Solvability of Magnetic Differential Equations

The calculation of both resistive and ideal plasma equilibria amounts to solving a number of magnetic differential equations which are of the type ~ B ·∇Φ = s. We apply the necessary and sufficient criterion for the existence of the potential Φ and find that a static equilibrium configuration of a magnetically confined plasma does not exist in axi-symmetric toroidal geometry. AMS classification...

Nonlinear Integro - Differential Equations

On d-solvability for linear differential equations

The aim of this paper is to investigate the possibility of solving a linear differential equation of degree n by means of differential equations of degree less than or equal to a fixed d, 1 ≤ d < n. This paper recovers and extends work of G. Fano, M. F. Singer and E. Compoint. Representations of algebraic Lie algebras are themain tool. © 2008 Elsevier Ltd. All rights reserved.

Application of the block backward differential formula for numerical solution of Volterra integro-differential equations

In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...

The Legendre Wavelet Method for Solving Singular Integro-differential Equations

In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.