It is well known that a damped or underrelaxed Newton's method will sometimes solve a system of nonlinear equations when the full Newton's method cannot. This happens, for example, when only a poor ...

Carpathian Journal of Mathematics, Vol. 31, No. 1 (2015), pp. 11-30 (20 pages) We use the method of recurrent functions to provide a new semilocal convergence analysis for secant-like methods in order ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...