The implicit block methods based on the backward differentiation formulae (BDF) for the solution of stiff initial value problems (IVPs) using variable step size is derived. We construct a variable step size block methods which will store all the coefficients of the method with a simplified strategy in controlling the step size with the intention of optimizing the performance in terms of precisi...

At the example of Hamiltonian differential equations, geometric properties of the flow are discussed that are only preserved by special numerical integrators (such as symplectic and/or symmetric methods). In the ‘non-stiff’ situation the long-time behaviour of these methods is well-understood and can be explained with the help of a backward error analysis. In the highly oscillatory (‘stiff’) ca...

In this paper, optimal control for stochastic linear quadratic singular neuro Takagi–Sugeno (T-S) fuzzy system with singular cost is obtained using genetic programming(GP). 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 GP approach. The obtained solution in t...

in this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $h(cdot,cdot)$-$phi$-$eta$-accretive operator in real  uniformly smooth banach spaces. it is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. this equivalence is used to define an iterative algorithm for solving fu...

A wind farm is a collection of wind turbines built in an area to provide electricity. Wind power is a renewable energy resource and an alternative to non-renewable fossil fuels. In this paper impact of wind farms in power system reliability is investigate and a new procedure for reliability assessment of wind farms in HL1 level is proposed. In proposed procedure, application of Fuzzy – Markov f...

This paper examines the implementation of simple combination mutation differential evolution algorithm for solving stiff ordinary equations. We use weighted residual method with a series expansion to approximate solutions solve problems from an equation linear and nonlinear problems. Then, we also implement our systems find that can exact solution smallest error each length have chosen. Thus, t...

Abstract Explicit stabilized integrators are an efficient alternative to implicit or semiimplicit methods avoid the severe time-step restriction faced by standard explicit applied stiff diffusion problems. In this paper we provide a fully discrete strong convergence analysis of family coupled with finite element for class parabolic semilinear deterministic and stochastic partial differential eq...

We propose a low Mach number, Godunov-type finite volume scheme for the numerical solution of the compressible Euler equations of gas dynamics. The scheme combines Klein’s non-stiff/stiff decomposition of the fluxes (J. Comput. Phys. 121:213-237, 1995) with an explicit/implicit time discretization (Cordier et al., J. Comput. Phys. 231:56855704, 2012) for the split fluxes. This results in a scal...