• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.409-438
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• 2000

In this paper we develop a new procedure to control stepsize for Runge- Kutta methods applied to both ordinary differential equations and semi-explicit index 1 differential-algebraic equation In contrast to the standard approach, the error control mechanism presented here is based on monitoring and controlling both the local and global errors of Runge- Kutta formulas. As a result, Runge-Kutta methods with the local-global stepsize control solve differential of differential-algebraic equations with any prescribe accuracy (up to round-off errors)

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.697-726
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• 1999

In this paper we develop a now procedure to control stepsize for linear multistep methods applied to semi-explicit index 1 differential-algebraic equations. in contrast to the standard approach the error control mechanism presented here is based on monitoring and contolling both the local and global errors of multistep formulas. As a result such methods with the local-global stepsize control solve differential-algebraic equation with any prescribed accuracy (up to round-off errors). For implicit multistep methods we give the minimum number of both full and modified Newton iterations allowing the iterative approxima-tions to be correctly used in the procedure of the local-global stepsize control. We also discuss validity of simple iterations for high accuracy solving differential-algebraic equations. Numerical tests support the the-oretical results of the paper.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.341-378
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• 1997

We consider three classes of numerical methods for solv-ing the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full a2nd modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and in-vestigate their efficiency in theory and practice.

• 대한수학회보
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• 제61권3호
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• pp.597-610
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• 2024

Using the Nevanlinna value distribution theory of algebroid functions, this paper investigates the growth of two types of complex algebraic differential equation with algebroid solutions and obtains two results, which extend the growth of complex algebraic differential equation with meromorphic solutions obtained by Gao [4].

• Journal of Mechanical Science and Technology
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• 제19권spc1호
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• pp.364-370
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• 2005

A stable walking pattern generation method for a biped robot is presented in this paper. In general, the ZMP (zero moment point) equations, which are expressed as differential equations, are solved to obtain a stable walking pattern. However, the number of differential equations is less than that of unknown coordinates in the ZMP equations. It is impossible to integrate the ZMP equations directly since one or more constraint equations are involved in the ZMP equations. To overcome this difficulty, DAE (differential and algebraic equation) solution method is employed. The proposed method has enough flexibility for various kinematic structures. Walking simulation for a virtual biped robot is performed to demonstrate the effectiveness and validity of the proposed method. The method can be applied to the biped robot for stable walking pattern generation.

• 대한기계학회논문집
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• 제18권9호
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• pp.2339-2348
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• 1994

The objective of this paper is to develop a solution method for the differential-algebraic equation(DAE) derived from constrained muti-body dynamic systems. Mechanical systems are often modeled as bodies and joints. Differential equations of motion are formulated for bodies. Since the bodies are connected by joint, the differential variables must satisfy the kinematic constraint equations that come from the joints. Difficulties are arised due to drift of the differential variables off the constraint equations. An optimization method is adopted to correct the drift of the differential variables. To demonstrate the efficiency of the proposed method a slider-crank mechanism is analyzed dynamically. Identical results are obtained as these from the commercial program DADS. Dynamic analysis of a High Mobility Multi-purpose Wheeled. Vehicle(HMMWV) is carried out to show the practicalism of the proposed method.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.951-969
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• 2012

In this paper, we propose a class of meshless collocation approaches for the solution of time dependent partial differential algebraic equations (PDAEs) in terms of a radial basis function interpolation numerical scheme. Kansa's method and the Hermite collocation method (HCM) for PDAEs are given. A sensitivity analysis of the solutions from different shape parameter c is obtained by numerical experiments. With use of the random collocation points, we have obtain the more accurate solution by the methods than those by the finite difference method for the PDAEs with index-2, i.e, we avoid the influence from an index jump of PDAEs in some degree. Several numerical experiments show that the methods are efficient.

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1141-1160
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• 2016

In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coeffcients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green's operator and the vector Green's function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권3호
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• pp.243-291
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• 2020

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 (MB₂ VMs). 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 MB₂ VMs introduced herein is a novel approach at developing very large scale integration methods (VLSIM) in the numerical solution of differential equations.

• 대한전자공학회논문지
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• 제16권5호
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• pp.18-26
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• 1979

본 논문에서는 algebraic matrix Lyapunov equations과 a1gebraic matrix Riccati equations에 관하여 잘 알려져 있는 중요한 결과를 확장한다. 본 연구는 Matrix 미분 방정식에서 양단 경계조건이 존재하는 문제를 다루며 여기에서 얻어지는 결과는 기존하고 있는 결과를 포함하게 된다. 특히 선형 시스템이 periodic feedback gain control로 안정화되는 필요충분조건을 구하며, two-point boundary Riccati equations의 해를 쉽게 구하는 반복 계산방법을 제시한다. 또한 interalwise reeceding horizon을 이용한 새로운 periodic feedback gain control이 시스템을 안전화시켜줌을 보여준다.