جستجوی مقالات مرتبط با کلیدواژه « ‎ritz method‎ » در نشریات گروه « ریاضی »

This paper focuses on the solvability and approximate analytic solution of composed linear descriptor operator with constant coefficient, using functional (Variational) approach. This approach is based on finding a suitable functional form whose critical points are the solution of the proposed problem and the solution of a proposed problem is a critical point of the obtained variational functional defined on suitable reflexive Hilbert space since the existence of this approach is based on the symmetry and positivity of the composed linear descriptor operator on Hilbert space. The necessary mathematical requirements are derived and proved. A step-by-step computational algorithm is proposed. Illustration and computation with the giving exact solution are also proposed.

An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage of the Ritz method is that it provides greater flexibility in which the boundary conditions are imposed at the end points of the interval. Furthermore, compared with the exact and eigenfunction solutions of the presented problems, the satisfactory results are obtained with low terms of basis elements. The convergence of the method is extensively discussed and finally two illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based on the spectral Ritz method‎. ‎Also‎, ‎two new methods are proposed for calculating the left Caputo fractional derivative and right Riemann-Liouville fractional derivative operators of the hybrid functions that are proportional to the Ritz method‎. ‎The FOCP is converted into a system of the algebraic equations by applying the fractional derivative operators and collocation method‎, ‎which determines the solution of the problem‎. ‎Error estimates for the hybrid function approximation‎, ‎fractional operators and‎, ‎the proposed method are provided‎. ‎Finally‎, ‎the efficiency of the proposed method and its accuracy in obtaining optimal solutions are shown by some test problems.