numerical solution of algebraic equations matlab

... Trang 1IMM DEPARTMENT OF MATHEMATICAL MODELLINGTechnical University of Denmark DK-2800 Lyngby – Denmark May 6, 1999 CBE Numerical Solution of Differential Algebraic Equations Editors: Claus ... Trang 9CHAPTER 1Introduction The (modern) theory of numerical solution of ordinary differential equations(ODEs) has been developed since the early part of this century – beginning withAdams, Runge ... stages of the step.In general these equations represents a non-linear system of equations The classical theory for determining the order of the local and global error isfound in a number of books

Ngày tải lên: 21/12/2016, 10:52

... University ofManchester for the degree of Doctor of Philosophy in the Faculty of Science. October 1989 Trang 21.1.3 the propagation of derivative discontinuitiesthrough systems of delay-differential equations ... the propagation of derivative discontinuities through systems of equations is presented Following a short resumd of standard techniques for the solution of ordinary differential equations (ODÉs), ... Delay-differential equations In this thesis we are concerned with the numerical solution of delay-differential equations (ĐÉs) Delay-differential equations may best be regarded as extensions of ordinary

Ngày tải lên: 11/10/2014, 04:02

... '',qci The Numerical Solution of Delay-differential Equations by David Richard Wile Department of Mathematics University of Manchester volume II of II A thesis submitted to the University of Manchester ... appendix we give a formal proof of the result (1.1.3:14). For any given time let the order of continuity of the component y i be Z i . Our task is thus to obtain a set of lower bounds {c i : > ... closure of E. Heuristically, by an extension of the above arguments, we may think of Ei as defining the set of points whose continuity bounds can affect the continuity bound, c i , of y i .

Ngày tải lên: 11/10/2014, 04:03

...            If the number of unknowns is equal to the number of equations, N=M, we may be able to solve the set of equations, provided that the equations are unique Gaussian Elimination ... elimination method in order to solve the set of equations and returns n values of x to the main program Test the program on the following set of equations: +27 = +6t +4s -2z +5y 3x -19 = -9t ... this method will be discussed below First, let’s review the concept of simultaneous linear equations A set of linear simultaneous equations may be written as: a11x1 + a12x2 + a13x3 + + a1N xN =

Ngày tải lên: 24/10/2014, 21:28

... FOR NUMERICAL SOLUTION OF FOR NUMERICAL SOLUTION OF THE mGRLW EQUATION THE mGRLW EQUATION THE mGRLW EQUATION Nguyen Van Tuan Hanoi Metropolitan University Abstract: In this paper, numerical ... B-spline for numerical solution of the modified equal width wave equation”, J Appl Math Inform., Vol 28(3 - 4), pp 611–624 10 A G Kaplan, Y Dereli (2017), “Numerical solutions of the GEW equation ... ≤ 1 Therefore, the linearized numerical scheme for the mGRLW equation is unconditionally stable Trang 64 NUMERICAL EXAMPLE We now obtain the numerical solution of the mGRLW equation for some

Ngày tải lên: 13/01/2020, 09:24

... studied in detail in [1] In the case of several terms, elements of the theory of corresponding Volterra equations of the first kind are presented in [2] Since the solution to (1)–(3) can be explicitly ... inevitable replacement of a large number of generating capacities In this regard, the problem of technical reequipment and dismantling of the main equipment of power plants is one of the most urgent ... Ti3(t) is the lifetime of the equipment of type i (the age of the oldest equipment of type i still in use at the moment t); x0(t) ≡ (x0(t), x0(t), x0(t)) is the known dynamics of commissioning the

Ngày tải lên: 12/02/2020, 18:26

... deflection of the symmetric rectangular support As said in the end of the previous subsection, for the problem of bending of the plate gi = 0 (i = 0, 3) We perform numerical experiments for plate of ... The rigorous theoretical proof of the convergence of the iterative method can be done in a similar way as the proof for one LPIS in [4] but due to the complexity of the internal supports we omit ... equations This is achieved due to the combination of a domain decomposition technique and a technique for reduction of the order of differential equations These techniques were used separately

Ngày tải lên: 26/03/2020, 02:04

... where U is numerical solution and u denotes exact solution.  Trang 6I = udx, I = (u + βu )dx, I   We have the exact solution of the MRLW is:  cosh (ρ(x − x − ct)),  The initial condition of Equation (1) given by:  ... = 1.  Therefore, the linearized numerical scheme for the MRLW equation is unconditionally  stable.  4 NUMERICAL EXAMPLE We now obtain the numerical solution of the MRLW equation for some problems. To  ... FOR NUMERICAL SOLUTION OF THE MRLW EQUATION Nguyen Van Dung 1 , Nguyen Viet Chinh 2 1 Hanoi National University of Education 2 Hanoi Metropolitan University Abstract: In this paper, numerical

Ngày tải lên: 28/06/2021, 19:39

... applications.) • Each of the first N locations of ija stores the index of the array sa that contains the first off-diagonal element of the corresponding row of the matrix (If there are no off-diagonal ... also be aware of some of the special sparse forms that occur in the solution of partial differential equations in two or more dimensions See Chapter 19 If your particular pattern of sparsity is ... pattern of sparsity of the matrix Patterns that occur frequently, or that are useful as way-stations in the reduction of more general forms, already have special names and special methods of solution

Ngày tải lên: 24/12/2013, 12:16

... Bounds for the Solution of the Algebraic Riccati Equations Komaroff 1994 in 16 obtained the following Let K be the positive semidefinite solution of the ARE1.4 Then the trace of K has the ... product of two general matrices The new trace bounds improve the previous results Then, we present some trace bounds for the solution of the algebraic Riccati equations, which improve some of the ... the solution of the AREsee 6 16 Moreover, in terms of 2,6, we know that an interpretation of trK is that trK/n is the average value of the optimal cost J∗as x0varies over the surface of

Ngày tải lên: 22/06/2014, 03:20

... Solution of non-linear algebraic equations 2.1 Introduction In the solution of linear problems by a finite element method we always need to solve a set of simultaneous algebraic equations of ... coefficient matrix is non-singular the solution to these equations is unique In the solution of non-linear problems we will always obtain a set of algebraic equations; however, they generally will ... convergent process for solutions of problems in which only one evaluation of * is made in each iteration Of course, this assumes that the initial solution is within the zone of attraction and, thus,

Ngày tải lên: 02/05/2018, 13:39

... Nonnegative Solution of Nonlinear Impulsive Differential Equations on Infinite Interval 1 Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China 2 School of ... economics The theory of impulsive differential equations has become an important area of investigation in the recent years and is much richer than the corresponding theory of differential equations For ... investigate the existence of minimal nonnegative solution for a class of second-order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times Consider

Ngày tải lên: 21/06/2014, 11:20

... the number of basic frequencies of ˙x  ψx, t, x ∈ R, is the same as that of basic frequencies of its unique solution Trang 2The spectrum containment of almost periodic solution of equationxt ... Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument Li Wang and Chuanyi Zhang Department of Mathematics, Harbin Institute of ... is a solution of 1.1, then xt  pxt − 1 are continuous at t ∈ R, which guarantees the uniqueness of solution of 1.1 and cannot be omitted To study the spectrum of almost periodic solution

Ngày tải lên: 21/06/2014, 20:20

... 2.6 ) admits a global solution. Proof Let ρ be a solution of (2.6) Thenρ ∈ ᐄ(P), the family of all solutions emanating u 1=max where u denotes the usual sup-norm ofu on [0, T] On the other ... paper as “the nature of the vec-tor field.” Therefore, a combination of properties of the associated vector field with theKneser’s property of the cross sections of the solutions’ funnel is the ... proposition, there is a solution ρ ∈ ᐄ(P) that solves the Taking into account the classical theorem of the extendability of solutions, we imposeone more condition on the desired solution lim Trang

Ngày tải lên: 22/06/2014, 22:20

... consisting of a system of ordinary differential equations (ODEs) and a system of algebraic equations so that we can use methods and results of the theory of ODEs Many results on stability properties of ... the theory of ODE we show that each solution of (3.1) is a solution of a linear equation of the form Trang 8A(t)x  + B(t)x + F (t)x = 0. (3.3)Theorem 3.1 Any nontrivial solution x0(t) of the perturbed ... initial value problem of (3.1) has a unique solution” (ii) Different solutions of (3.1) lead to different coefficient matrices of (3.3), hence they are solutions of different linear DAEs of type (3.3) Theorem

Ngày tải lên: 06/08/2014, 05:20

... 1994a, b). The purpose of this paper is to demonstrate that the basic objective of the canonical transformation, ie, the reduction of a large linear system of equations into sets of smaller, sparser ... values influence the right-hand side of the RAM equa-tions, which after canonical transformation is of the form: After each solution of the reduced system of equations, or after each iteration ... prediction of the missing ones at the current EM iteration, transformed records on the canonical scale can be computed After solution of the mixed model equations on the canonical scale and backsolution

Ngày tải lên: 09/08/2014, 18:22

... more accurate solutions • The size of the integration interval also influences the accuracy of the solutions (should be less than 10% of the time constant) • Solutions of sets of 1st order ODEs ... 21General form of ODE solution methods• New value = old value + integration interval × function of gradient • This is the basis for a family of algorithms used to provide numerical solutions of ODEs ... The order of the solution is given by ‘n’ • Theoretically, the higher the order of the solution, the more accurate is the method Trang 23Special cases of RK algorithmsGeneral form of RK algorithms

Ngày tải lên: 19/03/2015, 08:49

... Trang 4TABLE OF CONTENTSPage Acknowledgments i List of Tables viii List of Figures ix Chapters: 1 INTRODUCTION 1 2 TIME DOMAIN FINITE METHODS FOR SOLUTION OF MAXWELL’S EQUATIONS ... physical and mathematical properties of electromagnetic fields andMaxwell’s equations Finite methods are numerical techniques which seek solution ofMaxwell’s equations in the differential form ... applications of cient hybrid time domain finite methods for the numerical solution of time dependentMaxwell’s equations The two finite methods focused are FDTD and FETD methods.The applications of the

Ngày tải lên: 14/09/2015, 11:39

... Klein-Gordon-Schr¨odinger equations 26 3.1 Derivation of the Klein-Gordon-Schr¨odinger equations 26 3.2 Conservation laws of the Klein-Gordon-Schr¨odinger equations 28 3.3 Dynamics of mean value of the meson ... and soliton wave solutions of KGS 31 3.5 Reduction to the Schr¨odinger-Yukawa equations (S-Y) 32 4 Numerical studies of the Klein-Gordon-Schr¨odinger equations 34 4.1 Numerical methods ... Schr¨odinger-Yukawa equations 705.1 Introduction to the Schr¨odinger-Yukawa equations 705.2 Numerical method for the Schr¨odinger-Yukawa equations 725.3 Numerical results of the Schr¨odinger-Yukawa equations

Ngày tải lên: 27/11/2015, 11:19

... extension of both these theories, in this paper, we discuss DDAEs Suchequations, containing both algebraic constraints and delays arise, in particular, in thecontext of feedback control of DAE systems ... vanishes, then the pair (E, A) is regular and of index at most 1 Otherwise, the pair (E, A) is singular Consequently, the class of free equations and the class of equations with regular higher-index pair ... theory of DDAEs is much less well established;see [17, 18] for a recent analysis and the discussion of many of the difficulties Thisunsatisfactory situation is even more pronounced in the context of

Ngày tải lên: 16/12/2017, 02:57