In particular, we consider an

initial-value problem for the nonlocal model with initial data strictly compatible with the solitary wave solution of the KdV equation or the BBM equation and then use a finite-difference scheme to solve the

initial-value problem numerically.

In our ONR-funded study, we use a semianalytic Fourier-Laplace method to solve the complete

initial-value problem for linear waves forced by an idealized tsunami at the lower boundary.

to approximate the solution y(x) of the

initial-value problem at [x.

This kind of

initial-value problem of ODEs can be solved using numerical computation.

Equation (2) was first introduced in [12] and both global existence and blow-up results for solutions of the

initial-value problem with initial data in appropriate function spaces were established.

Taylor's expansion of a second-order

initial-value problemWhen an

initial-value problem is stiff, one will typically observe that a code based on an explicit scheme will need to use extremely small stepsizes in order to compute a stable solution as opposed to one based on an implicit scheme.

We present Fortran 90 software for the

initial-value problem in ordinary differential equations, including the interfaces and how Fortran 90 language features afford the opportunity both to address different types and structures of variables and to provide additional functionality.

Until the 1990s the inverse scattering methodology was pursued almost entirely for pure

initial-value problems.

Petzold, Numerical Solution of

Initial-Value Problems in Differential-Algebraic Equations, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1996.

The first three chapters cover

initial-value problems, and boundary-value problems solved using discrete variable methods or finite element methods, for ordinary differential equations.

12] Mahmouda and Osman, MS: On a class of spline-collocation methods for solving second-order

initial-value problems.