In this research we used forward-backward sweep method(FBSM) in order to solve optimal control problems. In this paper, one hybrid method based on ERK method of order 4 and 5 are proposed for the numerical approximation of the OCP. The convergence of the new method has been proved .This method indicate more accurate numerical results compared with those of ERK method of order 4 and 5 for solvin...

We construct and analyze robust strong stability preserving IMplicit–EXplicit Runge–Kutta (IMEX RK) methods for models of flow with diffusion as they appear in astrophysics, and in many other fields where equations with similar structure arise. It turns out that besides the optimization of the region of absolute monotonicity, some other properties of the methods are crucial for the success of s...

Unconditionally stable implicit time-marching methods are powerful in solving stiff differential equations efficiently. In this work, a novel framework to handle physical terms implicitly is proposed. Both and numerical stiffness originating from convection, diffusion source (typically related reaction) can be handled by set of predefined Time-Accurate highly-Stable Explicit (TASE) operators un...

In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the multi-stage homotopy perturbation method (MHPM). The MHPM is a technique adapted from the standard homotopy perturbation method (HPM) where standard HPM is converted into a hybrid numeric-analytic method called multistage homotopy perturbation method (HPM). The MHPM is tested for several exam...

The goal of this paper is focused on developing an efficient design strategy for simulating CNN arrays and hole-filling is implemented using RK step multistep methods to improve the performance of the image or handwritten character recognition. This approach is carried out by analyzing the important features of the hole-filler template and the dynamic process of CNN using well knownr RK step mu...

in this paper‎, ‎we propose a modification of the second order method‎ ‎introduced in [‎‎q. li and ‎x‎. ‎y. ‎wu‎, a two-step explicit $p$-stable method for solving second order initial value problems‎, ‎textit{‎appl‎. ‎math‎. ‎comput‎.}‎ {‎138}‎ (2003)‎, no. 2-3, ‎435--442‎] for the numerical solution of‎ ‎ivps for second order odes‎. ‎the numerical results obtained by the‎ ‎new method for some...

Most research on preconditioners for time-dependent PDEs has focused implicit multi-step or diagonally-implicit multi-stage temporal discretizations. In this paper, we consider monolithic multigrid fully-implicit Runge-Kutta (RK) time integration methods. These discretizations have very attractive accuracy and stability properties, but they couple the spatial degrees of freedom across multiple ...