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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.24 No.3
- 발행연도
- 2020.9
- 수록면
- 243 - 291 (49page)
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In this paper, multi-block generalized backward differentiation methods for numerical solutions of ordinary differential and differential algebraic equations are introduced. This class of linear multi-block methods is implemented as multi-block boundary value methods (MB₂VMs). The root distribution of the stability polynomial of the new class of methods are determined using the Wiener-Hopf factorization of a matrix polynomial for the purpose of their correct implementation. Numerical tests, showing the potential of such methods for output of multi-block of solutions of the ordinary differential equations in the new approach are also reported herein. The methods which output multi-block of solutions of the ordinary differential equations on application, are unlike the conventional linear multistep methods which output a solution at a point or the conventional boundary value methods and multi-block methods which output only a block of solutions per step. The MB₂VMs introduced herein is a novel approach at developing very large scale integration methods (VLSIM) in the numerical solution of differential equations.
목차
ABSTRACT
1. INTRODUCTION
2. THE SOLUTION OF MATRIX FINITE DIFFERENCE EQUATION
3. MULTI-BLOCK BOUNDARY VALUE METHODS (MB₂VMs)
4. CONSTUCTION OF THE MULTI-BLOCK GENERALIZED BACKWARD DIFFERENTIATION FORMULAS (MBGBDFS)
5. EFFECTS OF ADDITIONAL MULTIBLOCK METHODS ON THE STABILITY OF MB₂VMs AND MINIMUM BLOCK SIZE IMPLEMENTATION OF THE MB₂VMs
6. THE MBGBDFS (4.1) ON DIFFERENTIAL ALGEBRAIC EQUATIONS (DAES) AND NUMERICAL RESULTS
7. CONCLUSION, FURTHER AND FUTURE INVESTIGATION
REFERENCES
참고문헌 (53)
참고문헌 신청
E. Hairer / 1996 / Numerical methods for initial value problems in ordinary differential equations II / Springer
K. Brenan / 1989 / Numerical solution of initial-value problems in differential-algebraic equations / North-Holland
G. Dahlquist / 1963 / A special stability problem for linear multistep methods / BIT 3:27~43
M. Ihkile / 2007 / Stiffly stable continuous extension of second derivative LMM with an off-step points IVPs in ODEs / J Nig Assoc Math Phy 11:175~190
S. Ogunfeyitimi / 2016 / Implicit-Explicit Methods Based on Recursively Derived Second Derivative LMM / J. Nigerian Association of Mathematical Physics 38:57~66
K. Brenan / 1989 / Numerical solution of initial-value problems in differential-algebraic equations / North-Holland
G. Dahlquist / 1963 / A special stability problem for linear multistep methods / BIT 3:27~43
M. Ihkile / 2007 / Stiffly stable continuous extension of second derivative LMM with an off-step points IVPs in ODEs / J Nig Assoc Math Phy 11:175~190
S. Ogunfeyitimi / 2016 / Implicit-Explicit Methods Based on Recursively Derived Second Derivative LMM / J. Nigerian Association of Mathematical Physics 38:57~66
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