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
- Xavier Antoine, Christophe Besse, Jérémie Szeftel, Towards accurate artificial boundary conditions for nonlinear PDEs through examples , CUBO, A Mathematical Journal: Vol. 11 No. 4 (2009): CUBO, A Mathematical Journal
- Abolfazl Sadeghi, Ghasem Alizadeh Afrouzi, Maryam Mirzapour, Investigating the existence and multiplicity of solutions to \(\varphi(x)\)-Kirchhoff problem , CUBO, A Mathematical Journal: Vol. 26 No. 3 (2024)
- Charalampos Tsitouras, Explicit Runge-Kutta methods for the numerical solution of initial value problems , CUBO, A Mathematical Journal: Vol. 4 No. 2 (2002): CUBO, Matemática Educacional
- Meriem Djibaoui, Toufik Moussaoui, Variational methods to second-order Dirichlet boundary value problems with impulses on the half-line , CUBO, A Mathematical Journal: Vol. 24 No. 2 (2022)
- Filippo Cammaroto, Infinitely many solutions for a nonlinear Navier problem involving the \(p\)-biharmonic operator , CUBO, A Mathematical Journal: Vol. 24 No. 3 (2022)
- Weihui Wang, Zuodong Yang, Nonnegative solutions of quasilinear elliptic problems with sublinear indefinite nonlinearity , CUBO, A Mathematical Journal: Vol. 15 No. 2 (2013): CUBO, A Mathematical Journal
- Pierpaolo Natalini, Paolo Emilio Ricci, Bell Polynomials and some of their Applications , CUBO, A Mathematical Journal: Vol. 5 No. 3 (2003): CUBO, Matemática Educacional
- Ram U. Verma, Hybrid (Φ,Ψ,Ï,ζ,θ)−invexity frameworks and efficiency conditions for multiobjective fractional programming problems , CUBO, A Mathematical Journal: Vol. 17 No. 1 (2015): CUBO, A Mathematical Journal
- M. H. Saleh, S. M. Amer, M. A. Mohamed, N. S. Abdelrhman, Approximate solution of fractional integro-differential equation by Taylor expansion and Legendre wavelets methods , CUBO, A Mathematical Journal: Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal
- F. Brackx, H. De Schepper, V. Soucek, Differential forms versus multi-vector functions in Hermitean Clifford analysis , CUBO, A Mathematical Journal: Vol. 13 No. 2 (2011): 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.
