On scaled one-step methods

Block Implicit One - Step Methods

A class of one-step methods which obtain a block of r new values at each step are studied. The asymptotic behavior of both implicit and predictor-corrector procedures is examined.

One - way Large Range Step Methods forHelmholtz

A useful approach for long range computation of the Helmholtz equation in a waveguide is to re-formulate it as the operator diierential Riccati equation for the Dirichlet-to-Neumann (DtN) map. For waveguides with slow range dependence, the piecewise range independent approximation is used to derive a second order range stepping method for this one-way re-formulation. The range marching formulas...

Theory and Methods for One -step Odes

where f is continuous and outputs an Rd vector. approximation on grid functions Let y(t) be the true solution. LetH be the grid dened by step-sizes: h1 , . . . , hN such that 0 < t1 < . . . < tN satises t i = ∑ l=1 h i .1 Let ∣H∣ = maxi h i . 1 is is just the obvious grid where h i = t i − t i−1 . We are parameterizing it by the step-sizes h i instead of times because h is what shows up in th...

One step forward

One step forwards, one step back.