F-Operators for the Construction of Closed Form Solutions to Linear Homogenous PDEs with Variable Coefficients

A computational framework for the construction of solutions to linear homogenous partial differential equations (PDEs) with variable coefficients is developed in this paper. The considered class PDEs reads: ∂p∂t−∑j=0m∑r=0njajrtxr∂jp∂xj=0 F-operators are introduced and used transform original PDE into image PDE. Factorization solution rational exponential parts enables us construct analytic without direct integrations. number examples demonstrate efficiency proposed scheme.