Hybrid Functions in the Calculus of Variations
-
Mohsen Razzaghi
razzaghi@math.msstate.edu
-
Hamid-Reza Marzban
hmarzban@cc.iut.ac.ir
Downloads
Abstract
The solution of problems in the calculus of variations is obtained by using hybrid functions. The properties of the hybrid functions which consist of block-pulse functions plus legendre polynomials and block-pulse functions plus Chebyshev polynomials are presented. Two examples are considered, in the first example the brachistochrone problem is formulated as a nonlinear optimal control problem, and in the second example an application to a heat conduction problem is given. The operational matrix of integration in each case is introduced and is utilized to reduce the calculus of variations problems to the solution of algebraic equations. The method is general, easy to implement and yields very accurate results.
Keywords
Similar Articles
- M.I. Belishev, Dynamical Inverse Problem for the Equation ð’°áµ¼áµ¼ − Δ𒰠− ∇ln𜌠· ∇𒰠= 0 (the BC Method) , CUBO, A Mathematical Journal: Vol. 10 No. 2 (2008): CUBO, A Mathematical Journal
- Bapurao C. Dhage, Existence and Attractivity Theorems for Nonlinear Hybrid Fractional Integrodifferential Equations with Anticipation and Retardation , CUBO, A Mathematical Journal: Vol. 22 No. 3 (2020)
- Sapan Kumar Nayak, P. K. Parida, Global convergence analysis of Caputo fractional Whittaker method with real world applications , CUBO, A Mathematical Journal: Vol. 26 No. 1 (2024)
- Cheok Choi, Gen Nakamura, Kenji Shirota, Variational approach for identifying a coefficient of the wave equation , CUBO, A Mathematical Journal: Vol. 9 No. 2 (2007): CUBO, A Mathematical Journal
- Théodore K. Boni, Diabaté Nabongo, Quenching for discretizations of a nonlocal parabolic problem with Neumann boundary condition , CUBO, A Mathematical Journal: Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal
- Ioannis K. Argyros, Saïd Hilout, On the semilocal convergence of Newton–type methods, when the derivative is not continuously invertible , CUBO, A Mathematical Journal: Vol. 13 No. 3 (2011): CUBO, A Mathematical Journal
- Fouad Fredj, Hadda Hammouche, On existence results for hybrid \(\psi-\)Caputo multi-fractional differential equations with hybrid conditions , CUBO, A Mathematical Journal: Vol. 24 No. 2 (2022)
- Takahiro Sudo, Computing the Laplace transform and the convolution for more functions adjoined , CUBO, A Mathematical Journal: Vol. 17 No. 3 (2015): CUBO, A Mathematical Journal
- P. G. Patil, T. D. Rayanagoudar, S. S. Benchalli, Generalization of new continuous functions in Topological spaces , CUBO, A Mathematical Journal: Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal
- Helmuth R. Malonek, Dixan Peña, Frank Sommen, Fischer decomposition by inframonogenic functions , CUBO, A Mathematical Journal: Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal
<< < 1 2 3 4 5 6 7 8 9 10 11 12 > >>
You may also start an advanced similarity search for this article.
