TY - JOUR

T1 - Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations

AU - Butcher, J. C.

AU - Jackiewicz, Zdzislaw

N1 - Funding Information:
* Corresponding author. E-mail: jackiewi @math.la.asu.edu. 1 The work of this author was partially supported by the National Science Foundation under grant NSF DMS-92-08048.

PY - 1996/10

Y1 - 1996/10

N2 - We describe the construction of diagonally implicit multistage integration methods (DIMSIMs) of type 1 and 2 with the same stability properties as explicit Runge-Kutta methods or implicit SDIRK methods, respectively, of appropriate order. Such methods are intended for the numerical integration of nonstiff or stiff differential systems in a sequential computing environment. Examples of pqrst DIMSIMs are given with p, q, r,s ≤ 4 and t = 1 or 2, where p is the order, q is the stage order, r is the number of external stages, s is the number of internal stages, and t is the type of the method. Coefficients of the methods of order 4 were obtained numerically with the aid of continuation programs from PITCON, ALCON, and HOMPACK.

AB - We describe the construction of diagonally implicit multistage integration methods (DIMSIMs) of type 1 and 2 with the same stability properties as explicit Runge-Kutta methods or implicit SDIRK methods, respectively, of appropriate order. Such methods are intended for the numerical integration of nonstiff or stiff differential systems in a sequential computing environment. Examples of pqrst DIMSIMs are given with p, q, r,s ≤ 4 and t = 1 or 2, where p is the order, q is the stage order, r is the number of external stages, s is the number of internal stages, and t is the type of the method. Coefficients of the methods of order 4 were obtained numerically with the aid of continuation programs from PITCON, ALCON, and HOMPACK.

KW - A-stability

KW - General linear method

KW - Order conditions

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U2 - 10.1016/S0168-9274(96)00043-8

DO - 10.1016/S0168-9274(96)00043-8

M3 - Article

AN - SCOPUS:0030263281

SN - 0168-9274

VL - 21

SP - 385

EP - 415

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 4

ER -