<abstract><p>The numerical solution of an ordinary differential equation can be interpreted as the exact a nearby modified equation. Investigating behaviour solutions by analysing is known backward error analysis. If original and share structural properties, then approximate geometric features such existence conserved quantities. Conjugate symplectic methods preserve form Hamiltonia...

Diagonally split Runge–Kutta (DSRK) time discretization methods are a class of implicit time-stepping schemes which offer both high-order convergence and a form of nonlinear stability known as unconditional contractivity. This combination is not possible within the classes of Runge–Kutta or linear multistep methods and therefore appears promising for the strong stability preserving (SSP) timest...

Monotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal meth...

In object systems, classes take the role of modules, and interfaces consist of methods. Because methods are encapsulated in objects, interfaces in object systems do not allow abstracting over where methods are implemented. This implies that any change to the implementation structure may cause a rippling effect. Sometimes this unduly restricts the scope of software evolution, in particular for m...

in this paper, we will present a review of the multistep collocation method for delay volterra integral equations (dvies) from [1] and then, we study the superconvergence analysis of the multistep collocation method for dvies. some numerical examples are given to confirm our theoretical results.