The weak form of the SDOF and MDOF equation of motion, part I: Theory
<|reference_start|>The weak form of the SDOF and MDOF equation of motion, part I: Theory: The weak form of the SDOF and MDOF equations of motion are obtained. The original initial conditions problem is transformed into a boundary value problem. The boundary value problem is then solved and transformed back to the initial conditions one. Subsequently, a general method for obtaining numerical methods using an arbitrary number of linearly independent approximating functions is outlined.   This is part one of a series of three papers, in the second of which a numerical method is obtained, using Bernstein polynomials of arbitrarily high order. The numerical evidence for the convergence of the method will be presented in the third part paper.<|reference_end|>
@article{karaliolios2024the,
    title={The weak form of the SDOF and MDOF equation of motion, part I: Theory},
    author={Nikolaos Karaliolios and Dimitrios L. Karabalis},
    journal={arXiv preprint arXiv:2407.00441},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.00441},
    primaryClass={math.NA cs.NA}
}