A Continuation Problem for Computing Solutions of Discretised Evolution Problems. Part I -- Abstract Frame.

Tomas Ligursky (1) , Yves Renard (2)

1 MAaAM PrF UP - Department of Mathematical Analysis and Applications of Mathematics
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]

A continuation problem for finding successive solutions of discretised abstract evolution problems of the first order is proposed and a general piecewise $C^{1}$ continuation problem is studied. A condition ensuring local existence and uniqueness of its solution curves is given. An analogy of the first-order system for smooth problems is derived and results of existence and uniqueness of its solutions are stated. Possibility of continuation of a solution curve along a direction from the first-order system is discussed. A technique for numerical continuation of solution curves is developed.

Keywords: discretized evolution problem; continuation method; piecewise-smooth function; first-order system; predictor-corrector

Domains: Numerical Analysis [math.NA]; Solid mechanics [physics.class-ph]; Solid mechanics [physics.class-ph]

Tomas Ligursky, Yves Renard. A Continuation Problem for Computing Solutions of Discretised Evolution Problems. Part I -- Abstract Frame.. 2013. ⟨hal-00877716v1⟩