title: A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.
abstract: In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.
authors.affiliation: Department of Mathematics and Computer Science, Jigawa State University, Kafin Hausa, P.M.B 048, Kafin Hausa, Nigeria.
authors.forename: T A
authors.initials: TA
authors.lastname: Biala
authors.affiliation: Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044 USA.
authors.forename: S N
authors.initials: SN
authors.lastname: Jator
keywords: Boundary value methods; Hyperbolic and elliptic PDEs; Method of lines; Systems of ordinary differential equations