26 research outputs found
New approach to the solutions of the pib equation
In this paper, based on the Exp-function method and mathematical derivation, we obtain several explicit and exact traveling wave solutions for the PIB equation.Publisher's Versio
The meshless methods for numerical solution of the nonlinear Klein-Gordon equation
In this paper, we develop the numerical solution of nonlinear Klein-Gordon equation (NKGE) using the meshless methods. The finite difference scheme and the radial basis functions (RBFs) collocation methods are used to discretize time derivative and spatial derivatives, respectively. Numerical results are given to confirm the accuracy and efficiency of the presented schemes.Publisher's Versio
Developing a Bi-Level Structure for Evaluation of Regional Bank Branch Managers Focusing on their Consumption
Regional bank branch management is the most important elements of a bankâs structure. Each regional bank branch manager (RBBM) manages a large group of branches. In this paper, we develop a bi-level structure for the evaluation of RBBMs. In the developed bi-level structure, RBBMs are positioned at the upper level, and each RBBM has a group of branches located at the lower level. Generally, each RBBM, including their branches, tries to use inputs and produce outputs efficiently. However, each branch performs according to its goals and limited resources. The evaluation is a data envelopment analysis (DEA)-based model that focuses on the bankâs consumption perspective. We apply the suggested model to a real-world case study to evaluate five RBBMs, who altogether manage 110 branches in one of the expert banking systems
Collocation method based on modified âcubicâ B-spline âfor option pricing âmodels
Collocationââ âmethod âbased âon âmodifiedâ cubic B-spline functions âhas âbeen âdevelopedâ âfor âthe âvaluation âââof Europeanâ, âAmerican and Barrier options of single âasset. âThe ânew âapproach âcontains ââdiscretizing âofâ tââemporal âderivativeâ âusing âfinite âdifference âapproximations âand âapproximatingâ the option price with the âmodifiedâ B-spline functionsâ. âStability of this method has been discussed and shown that it is unconditionally stableâ. âThe âefficiency âof âtheâ âproposed âmethod âis âtested âby âdifferent âexamplesâââ.
Optimal homotopy asymptotic and homotopy perturbation methods for linear mixed volterra-fredholm ıntegral equations
Bu çalıĆmada, karma Volterra-Fredholm integral denklemleri optimal homotopi asimptotik metod (OHAM) ve Homotopi
Perturbasyon metodu (HPM) vasıtasıyla irdelenmiĆtir. YaklaĆımımız zamandan baÄımsız ve basit hesaplamalar yolu ile tam çözĂŒme
oldukça yaklaĆık çözĂŒmler veren bir yöntemdir. Bu iki yöntemin karĆılaĆtırılması tartıĆılmıĆtır. OHAM yaklaĆımının doÄruluÄu ve
etkinliÄi HPM çözĂŒmleri ile dört örnek kullanılarak karĆılaĆtırılmıĆtır. Sonuçlar OHAM ın HPM ye göre daha verimli ve esnek bir
yöntem olduÄunu göstermektedir.In this paper, we study the mixed Volterra-Fredholm integral equations of the second kind by means of optimal homotopy
asymptotic method (OHAM) and Homotopy Perturbation method (HPM).Our approach is independent of time and contains simple
computations with quite acceptable approximate solutions in which approximate solutions obtained by these methods are close to
exact solutions. Comparison of these methods have been discussed. The accuracy and efficiency of OHAM approach with respect to
Homotopy Perturbation method (HPM) is illustrated by presenting four test examples. The results indicate that the OHAM is very
effective and flexible to use with respect to HPM
Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation
This paper presents a numerical scheme based on the Galerkin finite element method and cubic B-spline base function with quadratic weight function to approximate the numerical solution of the time-fractional Burger's equation, where the fractional derivative is considered in the Caputo sense. The proposed method is applied to two examples by using the and error norms. The obtained results are compared with a previous existing method to test the accuracy of the proposed method
Numerical solutions of one-dimensional non-linear parabolic equations using Sinc collocation method
We propose a numerical method for solving singularly perturbed one-dimensional non-linear parabolic problems. The equation converted to the nonlinear ordinary differential equation by discretization first in time then subsequently in each time level we use the Sinc collocation method on the ordinary differential equation. The convergence analysis of proposed technique is discussed, and it is shown that the approximate solution converges to the exact solution at an exponential rate as well. We know that the conventional methods for these types of problems suffer due to decreasing of perturbation parameter, but the Sinc method handles such difficulty. For efficiency and accuracy of the method, we validate the proposed method by several examples. The numerical results confirm the theoretical behavior of the rates of convergence
Boubaker polynomials collocation approach for solving systems of nonlinear VolterraĂąFredholm integral equations
Numerical schemes have been developed for solutions of systems of nonlinear mixed VolterraĂąFredholm integral equations of the second kind based on the First Boubaker polynomials (FBPs). The classical operational matrices are derived. The unknown has been approximated by FBPs and the NewtonĂąCotes points were applied as the collocations points. Error estimate and convergence analysis of the proposed method have been proved. Some numerical experiments are considered. The results are compared with relevant studies in order to test the reliability, validity and effectiveness of the proposed approach. Keywords: First Boubaker polynomials, Best approximation, Operational matrix, Systems of VolterraĂąFredholm integral equations, Collocation method