A Novel Mathematical System For Resuming Dynamic Non-Linear Duffing - Holmes Problems

In this paper introducing novel mathematical approach to reduce the computational effort of non-linear problems and the technique called as novel technique. In this paper solve the Duffing and Duffing-Holmes equations by using novel technique is described clearly. This method consists of decomposing a given differential equation in to linear, non-linear and remainder terms. The method has been applied quite extensively by mathematicians for various cases. The convergence of this technique has been proved by using many engineering field problems and obtain result as good as analytical method. FEM, FDM and pdetool methods are considered for the same class of equation in comparison with Novel technique. In this report it is shown that the novel technique converges faster than other the FEM, FDM methods. Several linear differential equation problems are considered for illustrative purpose and the solutions of these problems are obtained. Solutions are also plotted from all these method in order to show the accuracy. The purpose of this seminar report is to see its application in various boundary value problems in linear differential equations and to see novel technique is giving stable and efficient results.The results from novel technique are compared with MATLAB solution, because of non-availability of exact solution. It could be classified as non-numerical method, although it looks like at least a semi-numerical one. It is much more accurate compared to most of the numerical methods. In this paper several problems are solved to check robustness of technique, improve the accuracy and convergence. The novel technique is quite efficient and is practically well suited for use in these problems. The novel technique is also a non-numerical method which can be adapted for solving Duffing and Duffing-Holmes equations. In the current paper, the principle of the decomposition method is described, and its advantages are shown solving Duffing and Duffing-Holmes equations. Several examples are given to check the reliability of the present method.