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 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 Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
S. N. Jator ◽  
F. F. Ngwane ◽  
N. O. Kirby
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Second Order ◽  
Hyperbolic Partial Differential Equations ◽  
Fixed Frequency ◽  
Block Method ◽  
Initial Value ◽  
Partial Differential ◽  
Predictor Corrector

We present a block hybrid functionally fitted Runge–Kutta–Nyström method (BHFNM) which is dependent on the stepsize and a fixed frequency. Since the method is implemented in a block-by-block fashion, the method does not require starting values and predictors inherent to other predictor-corrector methods. Upon deriving our method, stability is illustrated, and it is used to numerically solve the general second-order initial value problems as well as hyperbolic partial differential equations. In doing so, we demonstrate the method’s relative accuracy and efficiency.

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 Wendroff type inequalities for nonlinear hyperbolic equations

2001 ◽  
Vol 32 (4) ◽  
pp. 327-333
Author(s):  
Wen Rong Li ◽  
Sui Sun Cheng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Hyperbolic Equations ◽  
Hyperbolic Partial Differential Equations ◽  
Nonlinear Hyperbolic Equations ◽  
Initial Value ◽  
Partial Differential

Several Wendroff type inequalities are derived, and applications to characteristic initial value problems involving hyperbolic partial differential equations are illustrated.

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