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The four-point block hybrid collocation method is proposed to solve general third order ordinary differential equations directly. The main and additional methods are generated via interpolation and collocation of polynomial. These methods are implemented in block form to obtain the approximation at main points and off-step points concurrently. The stability properties are analyzed. Some famous problems are tested to illustrate the accuracy of the method. [ABSTRACT FROM AUTHOR]

In this research, we proposed an adaptation of hierarchical matrix (H-matrix) iterative based solution to solve the two-dimensional (2D) Poisson equation with Dirichlet boundary condition. The finite difference approximation, specifically the halfsweep iterative solver, is used to discretize the problem, which leads to a system of linear equation. The adaptation of H-matrix to the linear system leads to save memory utilization of the iterative solver. An experiment was conducted and the results were compared with the standard iterative method with the adaptation of H-matrix. The results show the superiority of the proposed method in terms of memory utilization and execution time. [ABSTRACT FROM AUTHOR]

Some new linear 3 and 5-step methods for solving special third order ordinary differential equations directly are constructed using Taylor's series expansion. A set of test problems are solved using the new method and the results are compared when the problem is reduced to a system of first order ordinary differential equations and then using the existing Runge-Kutta method. The numerical results have clearly shown the advantage and competency of the new methods. [ABSTRACT FROM AUTHOR]

A ninth order block hybrid collocation method is proposed for solving general second order ordinary differential equations directly. The derivation involves interpolation and collocation of basic polynomial that generates the main and additional methods. These methods are applied simultaneously to provide approximate solutions at five main points and three off-step points. The stability properties of the block method are discussed. Some illustrative examples are given to demonstrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

In this paper we derived a new diagonally implicit Runge-Kutta method of order four with minimum phase-lag for solving first order linear ordinary differential equation. The stability polynomial of the method is obtained and the stability region is presented. A set of problems are tested upon and numerical results proved that the method is more accurate compared to other well known methods in the scientific literature. [ABSTRACT FROM AUTHOR]

In this paper the fuzzy Improved Runge-Kutta method of order four for solving first-order fuzzy differential equations is proposed. The scheme is two step in nature and is based on fourth order Improved Runge-kutta method for solving first order ordinary differential equations. The numerical examples are tested to illustrate the efficiency of method. [ABSTRACT FROM AUTHOR]

In this paper, a new three-stage Runge-Kutta-Nyström (RKN) method with two variable coefficients is constructed. The new method is based on Garcia's RKN method of algebraic order four. By using the idea of dispersion and dissipation of order infinity, a new method for solving second-order ordinary differential equations (ODE) with periodic solutions is derived. Numerical tests show that the new method is more accurate than the other existing methods that were derived in the past. [ABSTRACT FROM AUTHOR]

We study fuzzy differential equations (FDEs) using the strongly generalized differentiability concept. Utilizing the characterization problem, we present approximate solutions of FDEs under Generalized differentiability by an equivalent system of ODEs. Then we extend midpoint approximation method and give its error, which guarantees pointwise convergence. An illustrative example is given. [ABSTRACT FROM PUBLISHER]