Numerical solution of arbitrary-order linear partial differential equations using an optimal control technique

2021 ◽  
Vol 187 ◽  
pp. 77-96
Author(s):  
Mazyar Zarepour ◽  
Ghasem Barid Loghmani
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Arbitrary Order ◽  
Control Technique ◽  
Partial Differential ◽  
Order Linear ◽  
Linear Partial Differential Equations

scholarly journals Optimal Control Theory for a System of Partial Differential Equations Associated with Stratified Fluids

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2672
Author(s):  
Edgardo Alvarez ◽  
Hernan Cabrales ◽  
Tovias Castro
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Theory ◽  
Optimal Solution ◽  
Necessary Condition ◽  
Stratified Fluids ◽  
Partial Differential ◽  
First Derivative ◽  
Linear Partial Differential Equations

In this paper, we investigate the existence of an optimal solution of a functional restricted to non-linear partial differential equations, which ruled the dynamics of viscous and incompressible stratified fluids in R3. Additionally, we use the first derivative of the considered functional to establish the necessary condition of the optimality for the optimal solution.

scholarly journals One Solution for Many Linear Partial Differential Equations With Terms of Equal Orders

2021 ◽  
Vol 4 (2) ◽  
pp. 21-27
Author(s):  
Lohans de Oliveira Miranda ◽  
Lossian Barbosa Bacelar Miranda
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Order Linear ◽  
Linear Partial Differential Equations ◽  
Straightforward Method

We disclose a simple and straightforward method of solving single-order linear partial differential equations. The advantage of the method is that it is applicable to any orders and the big disadvantage is that it is restricted to a single order at a time. As it is very easy compared to classical methods, it has didactic value.

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