A novel analytical approach for solving partial differential equations via a tensor product theory of Banach spaces
Waseem Ghazi Alshanti, Iqbal M. Batiha, Ma’mon Abu Hammad, Roshdi Khalil
Abstract
In this paper, we aim to propose a novel analytical method for obtaining atomic solutions to partial differential equations. A theory of tensor products in Banach spaces is utilized and some properties of atom operators are studied to achieve our goals. The proposed scheme is demonstrated through illustrative examples of inhomogeneous partial differential equations. The approach is indeed quite direct and effective in exactly solving partial differential equations.
Topics & Concepts
MathematicsTensor productPartial differential equationBanach spaceTensor (intrinsic definition)Mathematical analysisC0-semigroupStochastic partial differential equationDifferential equationApplied mathematicsPure mathematicsNumerical methods for differential equationsMatrix Theory and AlgorithmsNonlinear Waves and Solitons