Annihilation of loading parameters in classical numerical methods with differential equations
(EN)
Anastasselou, EG
(EN)
Ioakimidis, NI
(EN)
Classical numerical methods for the solution of applied mechanics and engineering problems usually lead to systems of linear algebraic equations. In the case when a parameter appears in the loading conditions, the same parameter appears also in the right-hand side of one or more than one of the aforementioned equations. Here the method of annihilation of this parameter, by applying appropriate linear differential operators to both sides of the linear algebraic equations including the parameter, is used. In this way, the whole problem can be solved by solving the resulting system of ordinary linear differential equations completely numerically, and symbolic computations are avoided. The case of Cauchy-type singular integral equations is used for the illustration of the method and related numerical results are presented. Further possibilities are also discussed in brief. Finally, the automatic derivation of the aforementioned annihilating operators, by using Gröbner bases, is considered.
(EN)
