Modified Variational Iteration Method for Second Order Initial Value Problems

In this paper, we introduce a modified variational iteration method for second order initial value problems by transforming the integral of iteration process. The main advantages of this modification are that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of conventional variational iteration method. The method is applied to some nonlinear second order initial value problems and the numerical results reveal that the modified method is accurate and efficient for second order initial value problems

Reproducing Kernel Method for Fractional Riccati Differential Equations

This paper is devoted to a new numerical method for fractional Riccati differential equations. The method combines the reproducing kernel method and the quasilinearization technique. Its main advantage is that it can produce good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results are compared with some existing methods to show the accuracy and effectiveness of the present method

On Higher Order Boundary Value Problems Via Power Series Approximation Method

In this work, a relatively new technique called Power Series Approximation Method (PSAM) is applied for the numerical approximate solution of non-linear higher order boundary value problems. Several examples are given to illustrate the efficiency and implementation of the method. The proposed method is efficient and effective on the experimentation as compared with the exact solutions. Numerical results are included to demonstrate the reliability and efficiency of the methods. Graphical representation of the obtained results reconfirms the potential of the suggested method. Keywords: Power series, nonlinear problems, boundary value problem, numerical simulatio

AN ENHANCED WAVELET BASED METHOD FOR NUMERICAL SOLUTION OF HIGH ORDER BOUNDARY VALUE PROBLEMS

The Legendre wavelet collocation method (LWCM) is suggested in this study for solving high-order boundary value problems numerically. Eighth, tenth, and twelfth-order examples are used as test problems to ensure that the technique is efficient and accurate. In comparison to other approaches, the numerical results obtained using LWCM demonstrate that the method's accuracy is very good. The results indicate that the method requires less computational effort to achieve better results

Improved Operational Matrices of DP-Ball Polynomials for Solving Singular Second Order Linear Dirichlet-type Boundary Value Problems

Solving Dirichlet-type boundary value problems (BVPs) using a novel numerical approach is presented in this study. The operational matrices of DP-Ball Polynomials are used to solve the linear second-order BVPs. The modification of the operational matrix eliminates the BVP\u27s singularity. Consequently, guaranteeing a solution is reached. In this article, three different examples were taken into consideration in order to demonstrate the applicability of the method. Based on the findings, it seems that the methodology may be used effectively to provide accurate solutions

A computational method for nonlinear 2m‐th order boundary value problems

In this paper, two point boundary value problems of 2mth‐order nonlinear differential equations are considered. The existence of the solution and a new iterative algorithm which is large‐range convergent are proposed for the problems in reproducing kernel space. The advantage of the approach must lie in the fact that, on the one hand, for the arbitrary fixed initial value function, the iterative method is convergent. On the other hand, the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives, respectively. Some examples are displayed to demonstrate the computation efficiency of the method. Foundation item: Supported by National Natural Science Foundation of China (No. 60572125); Heilongjiang Institute of Science and Technology (No. 07–17); Heilongjiang province education department science and technology (No. 11531324). First published online: 10 Feb 201