Invariant imbedding of linear partial differential equations via generalized Riccati transformations

Generalized Invariant Imbedding Relation.

Intertwining Laplace Transformations of Linear Partial Differential Equations

We propose a generalization of Laplace transformations to the case of linear partial differential operators (LPDOs) of arbitrary order in R . Practically all previously proposed differential transformations of LPDOs are particular cases of this transformation (intertwining Laplace transformation, ILT ). We give a complete algorithm of construction of ILT and describe the classes of operators in...

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Generalized power series solutions to linear partial differential equations

Let Θ = C[e−x1 , . . . , e−xn ][∂1, . . . , ∂n] and S = C[x1, . . . , xn][[eCx1+···+Cxn ]], where C is an effective field and xN 1 · · · x N n e Cx1+···+Cxn and S are given a suitable asymptotic ordering 4. Consider the mapping L : S → Sl ; f 7→ (L1 f, . . . , Ll f ), where L1, . . . , Ll ∈ Θ . For g = (g1, . . . , gl ) ∈ Sl L = im L , it is natural to ask how to solve the system L f = g. In th...

Computational technique of linear partial differential equations by reduced differential transform ‎method

This paper presents a class of theoretical and iterative method for linear partial differential equations. An algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. In this technique, the solution is calculated in the form of a series with easily computable components. There test modeling problems from mathematical mechanic, physi...