Block implicit one-step methods

Shampine, L. F.; Watts, H.A.

doi:10.1090/s0025-5718-1969-0264854-5

Cited by 166 publications

(48 citation statements)

References 8 publications

(4 reference statements)

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“…There are other block implicit schemes and several techniques for applying them ([3], [22], [26]). Here, we are primarily interested in the comparison of the mth order Runge-Kutta for all seasons [22] and the mth order block methods based on natural splines.…”

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confidence: 99%

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Integration formulas and schemes based on 𝑔-splines

Andria¹,

Byrne²,

Hill³

1973

Math. Comp.

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Abstract. Numerical integration formulas of interpolatory type are generated by the integration of g-splines. These formulas, which are best in the sense of Sard, are used to construct predictor-corrector and block implicit schemes. The schemes are then compared with Adams-Bashforth-Adams-Moulton and Rosser schemes for a particular set of prototype problems. Moreover, an improved error bound for linear multistep formulas based on g-splines and a comparison of L2 norms of Peano kernels for Adams and natural spline formulas are given.

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“…For co < 1, the block implicit natural spline method of order ms can be regarded as better than the Rosser method of order ms. Of course, hR and hs denote step size. For stability analyses, strategies for implementation, and convergence proof for block implicit methods, see [3], [22], and [26].…”

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confidence: 99%

Integration formulas and schemes based on 𝑔-splines

Andria¹,

Byrne²,

Hill³

1973

Math. Comp.

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“…The PC method of SHAMPINE and WATTS [9] is based on the block method of CLIPPINGER and DIMSDALE [1958], which can be presented in the form ( …”

Section: Predictor-corrector Methods Of Shampine and Wattsmentioning

confidence: 99%

Block Runge‐Kutta Methods on Parallel Computers

Houwen¹,

Sommeijer²

1992

Z Angew Math Mech

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“…A Linear Multistep Method is said to be zero stable if no root of the first characteristics polynomial has modulus greater than one and that any root with modulus one is simple [21]. …”

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Stability Analysis of the 2-Point Diagonally Implicit Super Class of Block Backward Differentiation Formula with Off-Step Points

Bature¹,

Musa²

2017

J Phys Math

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In this paper, the stability region of the 2-point diagonally implicit super class of block backward differentiation formula with off-step points is to obtain and demonstrate its suitability for solving stiff ODEs. The stability region must cover the entire negative half-plane for the method to be suitable for solving stiff differential equations, analysis also shows that the method is zero stable.

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Block implicit one-step methods

Abstract: Abstract. A class of one-step methods which obtain a block of r new values at each step are studied. The asymptotic behavior of both implicit and predictor-corrector procedures is examined.

Cited by 166 publications

References 8 publications

Integration formulas and schemes based on 𝑔-splines

Integration formulas and schemes based on 𝑔-splines

Block Runge‐Kutta Methods on Parallel Computers

Stability Analysis of the 2-Point Diagonally Implicit Super Class of Block Backward Differentiation Formula with Off-Step Points

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