Main Article Content
IN THIS ARTICLE, THIRD- AND FOURTH-ORDER ACCURATE EXPLICIT TIME INTEGRATION METHODS ARE PRESENTED FOR EFFECTIVE ANALYSES OF VARIOUS LINEAR AND NONLINEAR DYNAMIC PROBLEMS STATED BY SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN TIME. TWO SETS OF THE NEW METHODS ARE DEVELOPED BY EMPLOYING THE COLLOCATION APPROACH IN THE TIME DOMAIN. TO REMEDY SOME SHORTCOMINGS OF USING THE EXPLICIT RUNGE-KUTTA METHODS FOR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN TIME, THE NEW METHODS ARE DESIGNED TO INTRODUCE SMALL PERIOD AND DAMPING ERRORS IN THE IMPORTANT LOW-FREQUENCY RANGE. FOR LINEAR CASES, THE EXPLICITNESS OF THE NEW METHODS IS NOT AFFECTED BY THE PRESENCE OF NON-DIAGONAL DAMPING MATRIX. FOR THE NONLINEAR CASE, THE NEW METHODS CAN HANDLE VELOCITY DEPENDENT PROBLEMS EXPLICITLY WITHOUT DECREASING ACCURACY. THE NEW METHODS DO NOT HAVE ANY UNDETERMINED ALGORITHMIC PARAMETERS. IMPROVED NUMERICAL SOLUTIONS ARE OBTAINED WHEN THEY ARE APPLIED TO VARIOUS LINEAR AND NONLINEAR PROBLEMS.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).