We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential algebras. The algebraic treatment of boundary problems brings up two new algebraic structures whose symbolic representation and computational realization is base...

The notion of integro-differential algebra was introduced in [Rosenkranz, M. and Regensburger, G.: Solving and Factoring Boundary Problems for Linear Ordinary Differential Equations in Differential Algebras, J. Symbolic Comput., 2008(43/8), pp. 515–544] to facilitate the algebraic study of boundary problems for linear ordinary differential equations. In this report, we construct a discrete anal...

in this paper, some applications of the method of least squares (mls) for the solution of various problems in electromagnetics engineering is briefly reviewed. here, mls is employed for the solution of various problems such as solution of equations, curve fitting to measured data, generalized fourier coefficients, linear operator equations, inegro-differential equations, electrostatics and magn...

In this paper, a multipoint boundary value problem for systems of integro-differential equations with involution has been studied. To solve the studied problem, parameterization method is used. Based on parametrization method, decomposed into two parts, i.e., Cauchy and system linear equations. Necessary sufficient conditions unique solvability are determined.

in this paper, we consider an implicit block backwarddifferentiation formula (bbdf) for solving volterraintegro-differential equations (vides). the approach given in thispaper leads to numerical methods for solving vides which avoid theneed for special starting procedures. convergence order and linearstability properties of the methods are analyzed. also, methods withextensive stability region ...

We take as a starting point an ODE model for the spreading of a disease in a homogeneous population. We extend this model by introducing heterogeneities in the population, which yields a model including a PDE or an infinite dimensional system of ODEs. We show how these models can be reduced to a system of integro-differential equations and show a comparison of this system to the original ODE mo...

In this paper, we prove the existence of solutions of initial value problems for nth order nonlinear impulsive integro-differential equations of mixed type on an infinite interval with an infinite number of impulsive times in Banach spaces. Our results are obtained by introducing a suitable measure of noncompactness.

Keywords: Boundary value problems Differential-operator equations Banach-valued Besov spaces Operator-valued multipliers Interpolation of Banach spaces a b s t r a c t The boundary value problems for linear and nonlinear degenerate differential-operator equations in Banach-valued Besov spaces are studied. Several conditions for the separability of linear elliptic problems are given. Moreover, t...

In this article we have considered Fredholm integro-differential equation type second-order boundary value problems and proposed a rational difference method for numerical solution of the problems. The composite trapezoidal quadrature and non-standard difference method are used to convert Fredholm integro-differential equation into a system of equations. The numerical results in experiment on s...