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Math 361S Lecture Notes Numerical solution of ODEs
The following is a fundamental theorem about existence and uniqueness for ODE’s. Theorem 2.1. If f: [a;b] Rd!Rd is continuously di erentiable, then in a neigh-borhood [a;a+ ") around a, the solution to (2.1a){(2.1b) exists and is unique. Note that the solution may not exist for all t2[a;b] because the solution may diverge.
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