The trip back home was almost as smooth, after an initial problem.
Finally, respondents unanimously agreed (100%) that sequelae of an initial problem should be listed as a separate problem (Question #11).
(iii) In order to consider other generalizations and approaches for possible different applications, we can interpret the relaxation process either as an initial value problem or a memory problem.
The method of numerically integrating two-point asymptotic boundary value problem of the boundary layer type, the initial value method, requires that the problem be recast as an initial value problem.
In this case the problem can be formulated as an initial value problem: with initial conditions In general, the solution of Eq. (2) for the initial conditions in Eq. (3) and given boundary conditions can be found numerically.
Thus, the initial value problem (1.2) which describes the population problem studied by Verhulst, could be formulated instead as an initial value problem of a difference equation.
As we will explain below, the boundary value problem (1.2) can be regarded exactly as an initial value problem.
The full system of coupled nonlinear ODEs described above was solved as an initial value problem to steady state using MATLAB's 'ode15s' solver routine (a multi-step variable-order stiff problem solver that employs the numerical differentiation formulas scheme), with the relative error tolerance set at 10−6 (0.0001% accuracy) and an initial step size of 10−4.
Fundamentally, the system can be written as an initial value problem, sometimes referred to as a single-shoot approach [ 30], or as a multiple-shooting problem [ 31, 64].
Linear kinetic stability of a tokamak plasma is analyzed as an initial value problem.
The nonlinear equation is then numerically solved as an initial value problem on a periodic domain and different scenarios of surface structures are captured.
