K e y w o r d s O r d i n a r y differential equations, Initial value problems, Runge-Kut ta methods, Stiffness detection, Symbolic computation, Computer algebra systems, Computer generation of numerical methods. 1. I N T R O D U C T I O N A framework for explicit Runge-Kutta methods is being implemented as part of an ongoing overhaul of MATHEMATICA~S differential equation solver NDSolve. One o...

In this paper, optimal control for stochastic linear singular periodic neuro Takagi–Sugeno (T–S) fuzzy system with singular cost is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional ACP approach. ACP solution is equiv...

We present an easy to implement drift splitting numerical method for the approximation of stiff, nonlinear stochastic differential equations (SDEs). The method is an adaptation of the semi-implicit backward differential formula (SBDF) multistep method for deterministic differential equations and allows for a semi-implicit discretization of the drift term to remove high order stability constrain...

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method an...

in this paper, the variational iteration method for solving nth-order fuzzy integro differential equations (nth-fide) is proposed. in fact the problem is changed to the system of ordinary fuzzy integro-differential equations and then fuzzy solution of nth-fide is obtained. some examples show the efficiency of the proposed method.

Subject headings: Multirate time stepping / Local time stepping / Ordinary differential equations / Stiff differential equations / Asymptotic stability / High-order Rosenbrock methods / Partitioned Runge-Kutta methods / Mono-tonicity / TVD / Stability / Convergence. Het onderzoek dat tot dit proefschrift heeft geleid werd mede mogelijk gemaakt door een Peter Paul Peterichbeurs –verstrekt door d...

This paper presents a variable step size implicit numerical integration algorithm for dynamic analysis of stiff multibody systems. Stiff problems are very common in real world applications, and their numerical treatment by means of explicit integration is cumbersome or infeasible. Until recently, implicit numerical integration of the equations of motion of stiff mechanical systems has been prob...

A COmponent-based Methodology to derive Parallel programs to solve Ordinary Differential Equation (ODE) Solvers, termed COMPODES, is presented. The approach is useful to obtain distributed implementations of numerical algorithms which can be specified by combining linear algebra operations. The main contribution of the approach is the possibility of managing several implementations of the opera...

Rosenbrock methods are popular for solving stiff initial value problems for ordinary differential equations. One advantage is that there is no need to solve a nonlinear equation at every iteration, as compared with other implicit methods such as backward difference formulas and implicit Runge-Kutta methods. In this paper, we introduce some trust region techniques to control the time step in the...

One of the best ways for better understanding of biological experiments is mathematical modeling. Modeling cancer is one of the complicated biological modeling that has uncertainty. Therefore, fuzzy models have studied because of their application in achievement uncertainty in modeling. Overall, the main purpose of this modeling is creating a new view of complex phenomena. In this paper, fuzzy ...