Algebraic methods for the solution of linear functional equations

Algebraic methods for the solution of linear functional equations

Equation n ∑ i=0 aif(bix+ (1− bi)y) = 0 belongs to the class of linear functional equations. The solutions form a linear space with respect to the usual pointwise operations. According to the classical results of the theory they must be generalized polynomials. New investigations have been started few years ago. They clarified that the existence of non-trivial solutions depends on the algebraic...

Solution of linear partial differential equations by Lie algebraic methods

A new algorithm is proposed for obtaining explicit solutions of the Cauchy problem defined by a certain class of partial differential equations (PDE) of parabolic type. The algorithm exploits the algebraic structure of the problem to transform the PDE into an ordinary matrix differential equation, which is then solved by Lie algebraic techniques.

The Taylor Method for Numerical Solution of Fuzzy Generalized Pantograph Equations with Linear Functional Argument

ABS methods for nonlinear systems of algebraic equations

 Abstract    This paper gives a survey of the theory and practice of nonlinear ABS methods including various types of generalizations and computer testing. We also show three applications to special problems, two of which are new.

Solution of Systems of Linear Algebraic Equations