Tolga Güyer

A new method for computing the solutions of differential equation systems using generalized inverse via Maple

In J. Jones et al., J. Symbolic Comput. 25 (1998) 99-124, an algorithm for computing the generalized inverse of a singular rational matrix has been implemented in Maple. In this paper, we present a new symbolic algorithm to compute the initial value problem of higher order differential equations with constant coefficients using generalized inverse. The algorithm is subsequently implemented in the symbolic computational package Maple.

A symbolic and algebraic computation based Lambda-Boolean reduction machine via PROLOG

Abstract This paper presents a new Lambda-Boolean reduction machine for Lambda-Boolean and Lambda-Beta Boolean reductions in the context of Lambda Calculus and introduces the role of Church–Rosser properties and functional computation model in symbolic and algebraic computation with induction. The algorithm which improved for Lambda-Beta Boolean reduction is simulated by the efficient logical programming language Prolog.

A computational approach for the analytical solving of a Dirichlet-type problem for third order partial differential equations

This paper presents a new symbolic algorithm for computing an approximated analytic solution to a Dirichlet-type boundary-value problem for the third order partial differential equations using Galerkin method.

A functional computation model for the duality of two-variable Lambda-Boolean functions

This paper presents a new functional computation model for developing a class of two-variable Lambda-Boolean functions, and describes the properties of the duality principle on this model. With respect to this aim, some definitions and theorems which construct the model of the two-variable Lambda-Boolean functions are given. The simulation of the model is implemented in the programming language Prolog, and the whole code is given as an extended and revised version of the implementation in [S. Mirasyedioglu, T. Guyer, A symbolic and algebraic computation based Lambda-Boolean reduction machine via PROLOG, Appl. Math. Comput. 176 (1) (2006) 65-75].

A symbolic computation approach to a three-dimensional inverse problem for the transport equation

We consider a three-dimensional inverse problem for the transport equation and present a new symbolic algorithm for computing an approximated analytic solution to the problem. The algorithm has been implemented in the computer algebra system Maple.