Theory of Approximation and Applications
Volume:8 Issue: 1, Winter and Spring 2012

This paper gives an ecient numerical method for solving the nonlinear system of Volterra-Fredholm integral equations. A Legendre-spectral method based on the Legendre integration Gauss points and Lagrange interpolation is proposed to convert the nonlinear integral equations to a nonlinear system of equations where the solution leads to the values of unknown functions at collocation points.

In [1] we uniquely introduced ultra exponential functions (uxpa) and de ned next step of the serial binary operations: addition, multiplication and power. Also, we exhibited the topic of limit summability of real functions in [2,3]. In this paper, we study limit summability of the ultra exponential functions and prove some of their properties. Finally, we pose an unsolved problem about them.

In this paper, we prove the existence of fi xed point for J-type multi-valued map T in CAT(0) spaces and also we prove the strong convergence theorems for Ishikawa iteration scheme without using the xed point of involving map.

We obtain a sucint and nesessery theoreoms simple for compactness and weakly compactness of the best approximate sets by closed unit balls. Also we consider relations Kadec-Klee property and shur property with this objects. These theorems are extend of papers mohebi and Narayana.

In this paper boundedness and compactness of generalized composition operators from logarithmic Bloch type spaces to Q_K type spaces are investigated.

In this article, we apply this new method for solving an engineering system with initial and boundary conditions and integral criterion, and we will using dynamic programming as iteration for solving model.

We consider a new type of integrable coupled nonlinear Schrodinger (CNLS) equations proposed by our self [submitted to Phys. Plasmas (2011)]. The explicit form of soliton solutions are derived using the Hirota's bilinear method. We show that the parameters in the CNLS equations only determine the regions for the existence of bright and dark soliton solutions. Finally, through the linear stability analysis, the modulational instability condition is given.

In this paper, the di erential transform method (DTM) is applied to the Fisher equation. This method can be used to obtain the exact solutions of Fisher equation. Finally, we give some examples to illustrate the suciency of the method for solving such nonlinear partial di erential equations. These results show that this technique is easy to apply.