Changing stepsize in the integration of differential equations using modified divided differences

Krogh, Fred T.

doi:10.1007/bfb0066584

Cited by 42 publications

(41 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [3], the orientation was focused more on the ^i (n) which are the modified divided differences of w computed at t=tn.…”

Section: -46mentioning

confidence: 99%

“…If one is using the method outlined in [3] If one wants to approximate thesolution of a differential equation by a Chebyshev polynomial, and thus wants to get the coefficients for the integrated polynomial, one can save alittle computation by computing the integrated coefficients after the calculations indicated in (7) or (9). Thus for 3 s n < q-4 one has for 3 n , the n-th coefficient of ;he integrated polynomial…”

Section: -46mentioning

confidence: 99%

“…Modified divided d i fferences of the form used here were introduced in [2] and developed further in [3]. Shampine and Gordon use them in [4] and Jackson [5] has made a careful study of related computational approaches, concluding that the form used here is best.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Recurrence relations for computing with modified divided differences

Krogh

1979

Math. Comp.

Self Cite

View full text Add to dashboard Cite

Modified divided differences (MDD) provide a good way of representing a polynomial passing through points with unequally spaced abscissas. This note gives recurrence relations for computing coefficients in either the monomial or Chebyshev basis from the MDD coefficients, and for computing the MDD coefficients for either the differentiated or the integrated polynomial. The latter operation is likely to be useful if MDD are used in a method for solving stiff differential equations.

show abstract

“…In [3], the orientation was focused more on the ^i (n) which are the modified divided differences of w computed at t=tn.…”

Section: -46mentioning

confidence: 99%

Section: -46mentioning

confidence: 99%

See 1 more Smart Citation

Recurrence relations for computing with modified divided differences

Krogh

1979

Math. Comp.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [3], the presentation focused more on the <¡>¡(ri), which are the modified divided differences of w computed at t = tn, tn_x, . .…”

mentioning

confidence: 99%

“…, tn_i+x. To simplify notation, we will no longer explicitly include n when referring to the various parameters defined in (l)- (3). Note that for the case of constant stepsize, ß{ = 1 and the MDD reduce to backward differences.…”

mentioning

confidence: 99%

Recurrence Relations for Computing with Modified Divided Differences

Krogh¹

1979

Mathematics of Computation

Self Cite

View full text Add to dashboard Cite

Abstract.Modified divided differences (MDD) provide a good way of representing a polynomial passing through points with unequally spaced abscissas. This note gives recurrence relations for computing coefficients in either the monomial or Chebyshev basis from the MDD coefficients, and for computing the MDD coefficients for either the differentiated or the integrated polynomial. The latter operation is likely to be useful if MDD are used in a method for solving stiff differential equations.

show abstract

GPS-Based System for Satellite Tracking and Geodesy

Bertiger

Thornton

1989

Navigation

View full text Add to dashboard Cite

GPS offers significantly improved capabilities in precise positioning. Applications include 10 cm altitude determination for the Topex/Poseidon oceanographic satellite, centimeter positioning anywhere on the Earth, and precise attitude determination for synthetic aperture radar. In the pursuit of the most precise GPS-based measurements, NASA has sponsored the development of new software and hardware tools related to GPS. The dual-frequency Rogue receiver can track up to eight GPS satellites simultaneously. A new antenna design for the Rogue has reduced the combined effects of data noise and multipath to less than 15 cm peak with 2 min smoothing on the pseudorange. The corresponding contribution from data noise is less than 2 cm. Data noise for the carrier is insignificant, and multipath errors are about 1 cm for 2 min smoothing. The GPS Inferred Positioning System (GIPSY) is a software system that includes state-of-the-art Earth models, automatic data editing, and numerically stable and flexible square root filtering techniques for parameter estimation, including process noise modeling. With these tools, we have demonstrated submeter GPS orbits and measurements of positions on the Earth to a precision and accuracy of better than 20 parts per billion.

show abstract

Changing stepsize in the integration of differential equations using modified divided differences

Cited by 42 publications

References 11 publications

Recurrence relations for computing with modified divided differences

Recurrence relations for computing with modified divided differences

Recurrence Relations for Computing with Modified Divided Differences

GPS-Based System for Satellite Tracking and Geodesy

Contact Info

Product

Resources

About