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Local accuracy and error bounds of the improved Runge-Kutta numerical methods

Qureshi S., Memon Z., Shaikh A. A.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 4

73--84

In this paper, explicit Improved Runge-Kutta (IRK) methods with two, three and four stages have been analyzed in detail to derive the error estimates inherent in them whereas their convergence, order of local accuracy, stability and arithmetic complexity have been proved in the relevant literature. Using single and multivariate Taylor series expansion for a mathematical function of one and two variables respectively, slopes involved in the IRK methods have been expanded in order to obtain the general expression for the leading or principal term in the local truncation error of the methods. In addition to this, principal error functions of the methods have also been derived using the idea of Lotkin bounds which consequently gave rise to the error estimates for the IRK methods. Later, these error estimates were compared with error estimates of the two, three, and four-stage standard explicit Runge-Kutta (RK) methods to show the better performance of the IRK methods in terms of the error bounds on the constant step-size h used for solving the initial value problems in ordinary differential equations. Finally, a couple of initial value problems have been tested to determine the maximum absolute global errors, absolute errors at the final nodal point of the integration interval and the CPU times (seconds) for all the methods under consideration to get a better idea of how the methods behave in a particular situation especially when it comes to analyzing the error terms.

A simple semi-analytical model for the Kink effect for the intrinsic n-channel polysilico thin film transistors

Siddiqui M. J., Qureshi S., Alshariff S. M.

Electron Technology : Internet Journal

2007

Vol. 39, nr 1

1-4

In order to improve the modeling of Polysilicon thin film transistors (Poly-Si-TFTs) a precise evaluation of the excess current due to impact ionization is needed. In this paper we have proposed a simple model for the excess current resulting from the impact ionization occurring at high drain biases. Model is based on the estimation of the electric field in the saturated part of the channel. The electric field in the saturated region is obtained by the solution of the two- dimensional Poisson's equation. The model is semi-analytical and uses only one fitting parameter which is desirable for circuit simulation. The simulation results with the developed impact ionization current model are in excellent agreement with the available experimental output characteristics of the intrinsic n-channel Poly-Si-TFTs.