This paper extends the Implicit Determinant Method introduced by Spence & Poulton (J. Comput. Phys., 204 (2005), pp. 65-81) to obtain a numerical technique for the calculation of a 2-dimensional Jordan block in a parameter dependent matrix. An important feature of this technique is that the theory is straightforward to understand and an efficient numerical implementation is suggested naturally by the theory. Three interesting physical problems are presented arising from the panel flutter problem in aerodynamics, the stability of electrical power systems and a problem in quantum mechanics.
When finding numerical solutions to stiff and nonstiff initial value problems using linear multistep methods, ill-conditioned systems are often encountered. In this paper, we demonstrate how this ill-conditioning can be circumvented without iterative refinement or preconditioning, by carefully choosing the grid point used in deriving the discrete scheme from the continuous formulation. Results of numerical experiments show that the new scheme perform very well when compared with the exact solution and results from an earlier scheme.
In this paper, we state and prove the conditions for the non-singularity of the D matrix used in deriving the continuous form of the Two-step Butcher's hybrid scheme and from it the discrete forms are deduced. We also show that the discrete scheme gives outstanding results for the solution of stiff and non-stiff initial value problems than the 5 th order Butcher's algorithm in predictor-corrector form.
Aims/ Objectives: To compare the performance of four Sinc methods for the numerical approximation of indefinite integrals with algebraic or logarithmic end-point singularities.
Methodology: The first two quadrature formulas were proposed by Haber based on the sinc method, the third is Stengers Single Exponential (SE) formula and Tanaka et al.s Double Exponential (DE) sinc method completes the number. Furthermore, an application of the four quadrature formulas on numerical examples, reveals convergence to the exact solution by Tanaka et al.s DE sinc method than by the other three formulae. In addition, we compared the CPU time of the four quadrature methods which was not done in an earlier work by the same author.
Conclusion: Haber formula A is the fastest as revealed by the CPU time.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.