| 1. | In practice, the initial value problem is often solved numerically.
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| 2. | So the initial value problem has no unique solution in general relativity.
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| 3. | The most common approaches start with an initial value problem based on the ADM formalism.
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| 4. | For the equation and initial value problem:
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| 5. | The solution of the initial value problem in terms of characteristic variables is finally very simple.
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| 6. | Hiroshi Okamura obtained a necessary and sufficient condition for the solution of an initial value problem to be unique.
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| 7. | Given the coefficient matrix, one wishes to solve the initial value problem associated with the linear ordinary differential equation
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| 8. | For such spacetimes the equations in general relativity can be posed as an initial value problem on a Cauchy surface.
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| 9. | In this context, solving an initial value problem is interpreted as lying in the hyperplane given by the initial conditions.
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| 10. | For first order initial value problems, the Peano existence theorem gives one set of circumstances in which a solution exists.
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