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

Convergence of the Sinc method applied to Volterra integral equations

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method

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 bank’s 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 bank’s 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

B-Spline Method for Two-Point Boundary Value Problems

Abstract.In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary differential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate

Collocation method based on modified ‎cubic‎ B-spline ‎for option pricing ‎models

Collocation‎‎ ‎method ‎based ‎on ‎modified‎ cubic B-spline functions ‎has ‎been ‎developed‎ ‎for ‎the ‎valuation ‎‎‎of European‎, ‎American and Barrier options of single ‎asset. ‎The ‎new ‎approach ‎contains ‎‎discretizing ‎of‎ t‎‎emporal ‎derivative‎ ‎using ‎finite ‎difference ‎approximations ‎and ‎approximating‎ the option price with the ‎modified‎ B-spline functions‎. ‎Stability of this method has been discussed and shown that it is unconditionally stable‎. ‎The ‎efficiency ‎of ‎the‎ ‎proposed ‎method ‎is ‎tested ‎by ‎different ‎examples‎‎‎.

Optimal homotopy asymptotic and homotopy perturbation methods for linear mixed volterra-fredholm ıntegral equations

Bu çalışmada, karma Volterra-Fredholm integral denklemleri optimal homotopi asimptotik metod (OHAM) ve Homotopi Perturbasyon metodu (HPM) vasıtasıyla irdelenmiştir. Yaklaşımımız zamandan bağımsız ve basit hesaplamalar yolu ile tam çözüme oldukça yaklaşık çözümler veren bir yöntemdir. Bu iki yöntemin karşılaştırılması tartışılmıştır. OHAM yaklaşımının doğruluğu ve etkinliği HPM çözümleri ile dört örnek kullanılarak karşılaştırılmıştır. Sonuçlar OHAM ın HPM ye göre daha verimli ve esnek bir yöntem olduğunu 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

Sixth-order compact finite difference method for singularly perturbed 1D reaction diffusion problems

AbstractIn this paper, the sixth-order compact finite difference method is presented for solving singularly perturbed 1D reaction–diffusion problems. The derivative of the given differential equation is replaced by finite difference approximations. Then, the given difference equation is transformed to linear systems of algebraic equations in the form of a three-term recurrence relation, which can easily be solved using a discrete invariant imbedding algorithm. To validate the applicability of the proposed method, some model examples have been solved for different values of the perturbation parameter and mesh size. Both the theoretical error bounds and the numerical rate of convergence have been established for the method. The numerical results presented in the tables and graphs show that the present method approximates the exact solution very well

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 $L_2$ and ${L_\infty }$ error norms. The obtained results are compared with a previous existing method to test the accuracy of the proposed method