초기값 문제

노트

위키데이터

• ID : Q10167591

말뭉치

1. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem.
2. An older proof of the Picard–Lindelöf theorem constructs a sequence of functions which converge to the solution of the integral equation, and thus, the solution of the initial value problem.
3. Hiroshi Okamura obtained a necessary and sufficient condition for the solution of an initial value problem to be unique.
4. In the preceding pages we have developed several substantially different theories of initial value problems, using hypotheses of Lipschitz conditions, compactness, isotonicity, and dissipativeness.
5. Programs intended for non-stiff initial value problems perform very poorly when applied to a stiff system.
6. Although most initial value problems are not stiff, many important problems are, so special methods have been developed that solve them effectively.
7. With standard assumptions about the initial value problem, the cumulative effect grows no more than linearly for a one-step method.
8. It is inefficient and perhaps impractical to solve with constant step size an initial value problem with a solution that exhibits regions of sharp change.
9. See the section on initial value problems for an example of how this is achieved.
10. However, its success depends on a number of factors the most important of which is the stability of the initial value problem that must be solved at each iteration.
11. the corresponding initial value problems (beginning from either endpoint and integrating towards the other endpoint) are insufficiently stable for shooting to succeed.
12. The purpose of the present book is to solve initial value problems in classes of generalized analytic functions as well as to explain the functional-analytic background material in detail.
13. Most initial value problems for ordinary differential equations and partial differential equations are solved in this way.
14. A differential equation together with an initial condition is called an initial value problem.
15. A solution to an initial value problem is a solution to the differential equation that also satisfies the initial condition.
16. Explain why the following functions are not solutions to the given initial value problems.
17. An initial value problem is a problem that has its conditions specified at some time .
18. where denotes the boundary of , is an initial value problem.
19. The Initial Value Problems (IVPs) that we will study are essentially just antiderivatives with an initial condition applied, which allows us to obtain the value of " ", the constant of integration.
20. The particular solution of the initial value problem is a function that satisfies both the differential equation and the initial condition.
21. Explicit formulas for the solutions of initial value problems with both zero and nonzero initial functions are obtained.

메타데이터

위키데이터

• ID : Q10167591

Spacy 패턴 목록

• [{'LOWER': 'initial'}, {'LOWER': 'value'}, {'LEMMA': 'problem'}]
• [{'LOWER': 'cauchy'}, {'LEMMA': 'problem'}]