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• W201606064 abstract "This chapter focuses on the conversion of boundary-value problems into stable initial-value problems via several invariant imbedding algorithms. When the solution of the boundary-value problem is smooth and only a few output points are desired, all the algorithms operate with approximately the same degree of efficiency and return approximately the same accuracy. As a result of the stability of the equations, all of the codes normally produce greater accuracy than requested. The addition formulas, in particular, are especially susceptible to the number and placement of output points and to the strategy of choosing the break points to avoid the singularities. The Scott algorithm must be implemented with the restart process to avoid the loss of significance in subtraction. Since the imbedding algorithms are very stable and employ very sophisticated initial-value codes, which vary the step size, the integration is extremely efficient. The multiple shooting codes can be implemented to use the same initial-value codes. However, if the problem requires many subdivisions of the interval, then the number of equations becomes large and slows down the process. The imbedding will almost always be faster if there is much structure to the solution." @default.
• W201606064 created "2016-06-24" @default.
• W201606064 creator A5002279809 @default.
• W201606064 date "1975-01-01" @default.
• W201606064 modified "2023-09-26" @default.
• W201606064 title "ON THE CONVERSION OF BOUNDARY-VALUE PROBLEMS INTO STABLE INITIAL-VALUE PROBLEMS VIA SEVERAL INVARIANT IMBEDDING ALGORITHMS**Work supported by the U. S. Atomic Energy Commission" @default.
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• W201606064 doi "https://doi.org/10.1016/b978-0-12-068660-5.50008-9" @default.
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