Hira Soomro^1,*, Nooraini Zainuddin¹, Hanita Daud¹, Joshua Sunday²

CMC-Computers, Materials & Continua, Vol.72, No.2, pp. 2947-2961, 2022, DOI:10.32604/cmc.2022.025933 - 29 March 2022

Abstract Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost. The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency. Hybrid block methods for instance are specifically used in numerical integration of initial value problems. In this paper, an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations (ODEs). In deriving the method, the Lagrange interpolation polynomial was employed… More >

R.Kanapady¹, K.K.Tamma²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 189-208, 2004, DOI:10.3970/cmes.2004.006.189

Abstract An integrated design of generalized single step LMS methods for applications to nonlinear structural dynamics is described. The design of the mathematical framework encompasses all the traditional and new and recent optimal algorithms encompassing LMS methods, and readily permits the different a-form, v-form and d-form representations in a unique mathematical setting. As such, the theoretical developments and implementation aspects are detailed for subsequent applications to nonlinear structural dynamics problems. The developments naturally inherit a consistent treatment of nonlinear internal forces under the present umbrella of predictor multi-corrector generalized single step representations with a wide variety of algorithmic More >