Comparison of the Adomian decomposition method with homotopy perturbation method for the solutions of seventh order boundary value problems

The aim of this paper is to compare the Adomian decomposition method and the homotopy perturbation method for solving the linear and nonlinear seventh order boundary value problems. The approximate solutions of the problems obtained with a small amount of computation in both methods. Two numerical examples have been considered to illustrate the accuracy and implementation of the methods.  

Numerical solution of eighth order boundary value problems in reproducing Kernel space

In this paper, the approximate solutions to the eighth-order boundary-value problems are presented using the reproducing kernel space method. The procedure is applied on both linear and nonlinear problems. Searching least value (SLV) method is investigated for nonlinear boundary value problems. The argument is based on the reproducing kernel space $W_{2}^{9}[a,b]$ . The approach provides the solution in the form of a convergent series with easily computable components. Analytical results are given for several examples to illustrate the implementation and efficiency of the method. A comparison of the results obtained by the present method with results obtained by other methods reveals that the present method is more effective and convenient.  

Modified form of binary and ternary 3-point subdivision schemes

Binary 3-point scheme, developed by Hormann and Sabin [Hormann, K. and Sabin, Malcolm A., 2008, A family of subdivision schemes with cubic precision, Computer Aided Geometric Design, 25, 41-52], has been modified by introducing a tension parameter which generates a family of C¹ limiting curves for certain range of tension parameter. Ternary 3-point scheme, introduced by Siddiqi and Rehan [Siddiqi, Shahid S. and Rehan, K., 2009, A ternary three point scheme for curve designing, International Journal of Computer Mathematics, In Press, DOI: 10.1080/00207160802428220], has also been modified by introducing a tension parameter which generates family of C¹ and C² limiting curves for certain range of tension parameter. Laurent polynomial method is used to investigate the continuity of the subdivision schemes. The performance of modified schemes has been demonstrated by considering different examples along with its comparison with the established subdivision schemes.