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
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
This kind of initial-value problem
of ODEs can be solved using numerical computation.
Equation (2) was first introduced in  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 problem
When 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