initial value problem in a sentence

Examples

1. In 1988, Rudolf Lohner developed Fortran-based software for reliable solutions for initial value problems using ordinary differential equations.
2. He discovered the necessary and sufficient conditions on initial value problems of ordinary differential equations for the solution to be unique.
3. Any differential equation will have many solutions, and each constant represents the unique solution of a well-posed initial value problem.
4. If L _ 1 and L _ 2 were constant coefficient matrices, then the exact solution to the associated initial value problem would be
5. Do you mean generating N different \ Delta \ mathbf { u } ( 0 ) s and solving an initial value problem with them.
6. If we cut out this singularity with a cutoff function, then the so obtained operators still provide solutions to the initial value problem modulo smooth functions.
7. Then the above initial / boundary value problem can be interpreted as an initial value problem for an ordinary differential equation on the space " X ":
8. General solutions of the spatially periodic initial value problem for the heat equation may be obtained by convolving the initial data at 0 } } with the theta function.
9. Then the solution on the interval [ 0, \ tau ] is given by \ psi ( t ) which is the solution to the inhomogeneous initial value problem
10. for some " h "  "  ! where " the " solution to the above equation and initial value problem can be found.