Abstract: Bringing forth a survey on recent higher order spline
techniques for solving boundary value problems in ordinary
differential equations. Here we have discussed the summary of the
articles since 2000 till date based on higher order splines like Septic,
Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree
splines. Comparisons of methods with own critical comments as
remarks have been included.
Abstract: Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.