Differential — Operator Solutions for Complex Partial Differential Equations

1999 ◽  
pp. 29-40
Author(s):  
O. Celebi ◽  
Sare Sengül
Keyword(s):  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Partial Differential

scholarly journals On some stochastic parabolic differential equations in a Hilbert space

2005 ◽  
Vol 2005 (2) ◽  
pp. 167-173 ◽  
Author(s):  
Khairia El-Said El-Nadi
Keyword(s):  
Hilbert Space ◽  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Partial Differential Operator ◽  
Parabolic Differential Equations ◽  
Partial Differential ◽  
Mixed Problems ◽  
Uniqueness Of The Solution ◽  
Weiner Process

We consider some stochastic difference partial differential equations of the form du(x,t,c)=L(x,t,D)u(x,t,c)dt+M(x,t,D)u(x,t−a,c)dw(t), where L(x,t,D) is a linear uniformly elliptic partial differential operator of the second order, M(x,t,D) is a linear partial differential operator of the first order, and w(t) is a Weiner process. The existence and uniqueness of the solution of suitable mixed problems are studied for the considered equation. Some properties are also studied. A more general stochastic problem is considered in a Hilbert space and the results concerning stochastic partial differential equations are obtained as applications.

scholarly journals New Approach for Solving Partial Differential Equations Based on Collocation Method

2020 ◽  
Vol 18 ◽  
pp. 118-128
Author(s):  
Alaa Almosawi ◽  
Luma N. M. Tawfiq
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Collocation Method ◽  
Linear Differential Operator ◽  
Partial Differential ◽  
Restrictive Assumption ◽  
New Approach ◽  
Linear Differential

In this paper, a new approach for solving partial differential equations was introduced. The collocation method based on LA-transform and proposed the solution as a power series that conforming Taylor series. The method attacks the problem in a direct way and in a straightforward fashion without using linearization, or any other restrictive assumption that may change the behavior of the equation under discussion. Five illustrated examples are introduced to clarifying the accuracy, ease implementation and efficiency of suggested method. The LA-transform was used to eliminate the linear differential operator in the differential equation.

scholarly journals On solving initial value problems for partial differential equations in maple

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Srinivasarao Thota
Keyword(s):  
Applied Sciences ◽  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Partial Differential Operator ◽  
Initial Value ◽  
Partial Differential ◽  
Greens Function ◽  
The Given

Abstract Objectives In this paper, we present and employ symbolic Maple software algorithm for solving initial value problems (IVPs) of partial differential equations (PDEs). From the literature, the proposed algorithm exhibited a great significant in solving partial differential equation arises in applied sciences and engineering. Results The implementation include computing partial differential operator (), Greens function () and exact solution () of the given IVP. We also present syntax, , to apply the partial differential operator to verify the solution of the given IVP obtained from . Sample computations are presented to illustrate the maple implementation.

scholarly journals The Cauchy Problem For Linear Partial Differential Equations With Restricted Boundary Conditions

1956 ◽  
Vol 8 ◽  
pp. 426-431 ◽  
Author(s):  
E. P. Miles ◽  
Ernest Williams
Keyword(s):  
Cauchy Problem ◽  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Cauchy Data ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
The Cauchy Problem ◽  
Image Position

We shall discuss solutions of linear partial differential equations of the form1where Ψ is an ordinary differential operator of order s with respect to t. Our first theorem gives a solution of (1) for the Cauchy data;2j = 1,2, ߪ,s − 1,whenever the function P is annihilated by a finite iteration of the operator Φ.

scholarly journals ABOUT SOME SUPPLEMENTARY POSSIBILITY FOR NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

2016 ◽  
Vol 11 (1) ◽  
pp. 75-78
Author(s):  
A. B. Chaadaev
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Numerical Solution ◽  
Third Order ◽  
Laplace Operators ◽  
Partial Differential ◽  
The Difference

A substitution of an non-homogeneous term and of a differential operator by the difference of Laplace operators in the direct co-ordinate system and in the turned one in the partial differential equations of first, second and third order is proposed. The numerical solution obtained by solving the substituting equation corresponds to the exact solution of the initial equations.

scholarly journals An uncoupling procedure for a class of coupled linear partial differential equations

1985 ◽  
Vol 26 (4) ◽  
pp. 503-516 ◽  
Author(s):  
A. McNabb
Keyword(s):  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Large Class ◽  
Partial Differential Operator ◽  
Coupled System ◽  
System Of Equations ◽  
Partial Differential ◽  
Similar System ◽  
Linear Partial Differential Equations

AbstractA Fredholm operator exists which maps the solutions of a system of linear partial differential equations of the form ∂u/∂t = DLu + Au coupled by a matrix A onto those solutions of a similar system coupled by a matrix B which have the same initial values. The kernels of this operator satisfy a hyperbolic system of equations. Since these equations are independent of the linear partial differential operator L, the same operator serves as a mapping for a large class of equations. If B is chosen diagonal, the solutions of a coupled system with matrix A may be obtained from the uncoupled system with matrix B.

scholarly journals Generalized q-Laguerre type polynomials and q-partial differential equations

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1403-1415
Author(s):  
Da-Wei Niu
Keyword(s):  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Generating Functions ◽  
Final Section ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Partial Differential ◽  
Integral Formulas ◽  
Special Cases

In this paper we define the q-Laguerre type polynomials Un(x; y; z; q), which include q-Laguerre polynomials, generalized Stieltjes-Wigert polynomials, little q-Laguerre polynomials and q-Hermite polynomials as special cases. We also establish a generalized q-differential operator, with which we build the relations between analytic functions and Un(x; y; z; q) by using certain q-partial differential equations. Therefore, the corresponding conclusions about q-Laguerre polynomials, little q-Laguerre polynomials and q-Hermite polynomials are gained as corollaries. As applications, some generating functions and generalized Andrews-Askey integral formulas are given in the final section.

scholarly journals On the existence of optimal control for controlled stochastic partial differential equations

1989 ◽  
Vol 115 ◽  
pp. 73-85 ◽  
Author(s):  
Noriaki Nagase
Keyword(s):  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Admissible Control ◽  
Order Differential Operator ◽  
Control Problems ◽  
Partial Differential ◽  
The Cauchy Problem ◽  
Existence Of Optimal Control

In this paper we are concerned with stochastic control problems of the following kind. Let Y(t) be a d’-dimensional Brownian motion defined on a probability space (Ω, F, Ft, P) and u(t) an admissible control. We consider the Cauchy problem of stochastic partial differential equations (SPDE in short)where L(y, u) is the 2nd order elliptic differential operator and M(y) the 1st order differential operator.

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