scholarly journals Shooting methods for numerical solutions of control problems constrained by linear and nonlinear hyperbolic partial differential equations

2004 ◽  
Author(s):  
Sung-Dae Yang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Hyperbolic Partial Differential Equations ◽  
Control Problems ◽  
Shooting Methods ◽  
Partial Differential ◽  
Linear And Nonlinear

scholarly journals On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
E. E. Eladdad ◽  
E. A. Tarif
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Partial Differential ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

In the current work, a combination between a new integral transform and the homotopy perturbation method is presented. This combination allows to obtain analytic and numerical solutions for linear and nonlinear systems of partial differential equations.

scholarly journals On a Computational Method for Non-integer Order Partial Differential Equations in Two Dimensions

2019 ◽  
Vol 12 (1) ◽  
pp. 39-57
Author(s):  
Muhammad Ikhlaq Chohan ◽  
Kamal Shah
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Jacobi Polynomials ◽  
Two Dimensions ◽  
Computational Method ◽  
Hyperbolic Partial Differential Equations ◽  
Unknown Coefficient ◽  
Operational Matrices ◽  
Partial Differential

This manuscript is concerning to investigate numerical solutions for different classesincluding parabolic, elliptic and hyperbolic partial differential equations of arbitrary order(PDEs). The proposed technique depends on some operational matrices of fractional order differentiation and integration. To compute the mentioned operational matrices, we apply shifted Jacobi polynomials in two dimension. Thank to these matrices, we convert the (PDE) under consideration to an algebraic equation which is can be easily solved for unknown coefficient matrix required for the numerical solution. The proposed method is very efficient and need no discretization of the data for the proposed (PDE). The approximate solution obtain via this method is highly accurate and the computation is easy. The proposed method is supported by solving various examples from well known articles.

Steady Gravity Flow of Frictional-Cohesive Solids in Converging Channels

1964 ◽  
Vol 31 (1) ◽  
pp. 5-11 ◽  
Author(s):  
A. W. Jenike
Keyword(s):  
Partial Differential Equations ◽  
Stress Field ◽  
Differential Equations ◽  
Radial Stress ◽  
Numerical Solutions ◽  
Yield Function ◽  
Hyperbolic Partial Differential Equations ◽  
Stress Fields ◽  
Special Importance ◽  
Partial Differential

Frictional-cohesive solids such as soil, ores, chemicals, sugar, flour are regarded as plastic and represented by the Jenike-Shield yield function [1] during steady flow. The stress-strain rate relations are based on isotropy, continuity, and a one-to-one dependence of density on the major pressure. In plane strain and in axial symmetry the stress field requires the solution of a system of two hyperbolic partial differential equations. The velocity field can then be computed by solving another system of two linear homogeneous partial differential equations of the hyperbolic type. In straight conical channels, a particular stress field called the “radial stress field” assumes a special importance because evidence has been presented elsewhere that all general fields tend to approach the radial stress fields in the vicinity of the vertex. Examples of numerical solutions of radial stress fields are given.

scholarly journals A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

1995 ◽  
Vol 36 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Mohammad A. Kazemi
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problems ◽  
Fréchet Derivative ◽  
Necessary Condition ◽  
Control Problems ◽  
Partial Differential ◽  
Frechet Derivative ◽  
First Order

AbstractIn this paper a class of optimal control problems with distributed parameters is considered. The governing equations are nonlinear first order partial differential equations that arise in the study of heterogeneous reactors and control of chemical processes. The main focus of the present paper is the mathematical theory underlying the algorithm. A conditional gradient method is used to devise an algorithm for solving such optimal control problems. A formula for the Fréchet derivative of the objective function is obtained, and its properties are studied. A necessary condition for optimality in terms of the Fréchet derivative is presented, and then it is shown that any accumulation point of the sequence of admissible controls generated by the algorithm satisfies this necessary condition for optimality.

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