In this work we discuss a class of defect correction methods which is easily adapted to create parallel time integrators for multi-core architectures and is ideally suited for developing methods which can be order adaptive in time. The method is based on Integral Deferred Correction (IDC), which was itself motivated by Spectral Deferred Correction by Dutt, Greengard and Rokhlin (BIT-2000). The ...

in this paper, we present a comparative study between the adomian decomposition method and two classical well-known runge-kutta and central difference methods for the solution of damped forced oscillator problem. we show that the adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply.

In this paper, we solve the MOSFET RF circuit ordinary differential equations with the waveform relaxation method, monotone iterative method, and Runge-Kutta method. With the monotone iterative method, we prove each decoupled and transformed circuit equation converges monotonically. This method provides an alternative in the time domain numerical solution of MOSFET RF circuit equations.

In this paper, optimal control for stochastic linear singular Takagi–Sugeno (T–S) fuzzy delay system with quadratic performance 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 GP solution is equivale...

Boundary value problems arise in many applications, and shooting methods are one approach to approximate the solution of such problems. A Shooting method transforms a boundary value problem into a sequence of initial value problems, and takes the advantage of the speed and adaptivity of initial value problem solvers. The implementation of continuous Runge-Kutta methods with defect control for i...