Extended one-step schemes of exponential type are introduced for the numerical solution of stiff initial-value problems. These schemes are uniformly convergent of third and fourth orders of accuracy. In addition, we show that these schemes are optimal when ϵ→ 0. Numerical results and comparisons with other schemes are presented.

Extended one-step schemes of exponential type are introduced for solving singularly perturbed Volterra integro-differential problems. These schemes are of order (m+ 1), m= 0, 1, 2,…, when the perturbation parameter, ε, is fixed. These schemes have the property that if ε is of order h they reduced to first order of accuracy and optimal when ε→ 0. Stability analysis of these schemes are presented. Numerical results and comparisons with other schemes are presented.

Extended one-step schemes of exponential type are introduced for solving singularly perturbed Volterra integro-differential problems. These schemes are of order (m+ 1), m= 0, 1, 2,…, when the perturbation parameter, ε, is fixed. These schemes have the property that if ε is of order h they reduced to first order of accuracy and optimal when ε→ 0. Stability analysis of these schemes are presented. Numerical results and comparisons with other schemes are presented.

We have assessed the accuracy of a simplified integral equation (SIE) modeling approach for marine controlled-source electromagnetics (CSEM) with low applied frequencies and a resistive target. The most computationally intensive part of rigorous integral equation (IE) modeling is the computation of the anomalous electric field within the target itself. This leads to a matrix problem with a dense coefficient matrix. It is well known that, in general, the presence of many grid cells creates a computational disadvantage for dense-matrix

The emission properties of CeB6 compared to LaB6 thermionic cathodes have been measured using an electrostatic DC gun. Obtaining knowledge of the emission properties is the first step in understanding the back-bombardment effect that limits wide usage of thermionic radio-frequency electron guns. The effect of back-bombardment electrons on CeB6 compared to LaB6 was studied using a numerical simulation model. The results show that for 6 ls pulse duration with input radio-frequency power of 8 MW, CeB6 should experience 14% lower temperature increase and 21% lower current density rise compared to LaB6. We conclude that CeB6 has the potential to become the future replacement for LaB6 thermionic cathodes in radio-frequency electron guns