methods for solving integral equations

... accurate RK methods, i.e.,for methods satisfying asi = bi for i = 1, , s we have yn+1 = Yns.Therefore g(yn+1) = 0 is automatically satisfied for such methods sincefrom (2.7b) for i = s we ... thesis Therefore, this thesis concentrates on numerical methods for semi-explicitDAEs of index 2 Here, we are concerned with one-step methods for index 2 DAEs in senberg form These methods combine ... meth-ods have been developed for DAEs Most numerical methods for differentialalgebraic equations based on standard methods from the theory of ordinarydifferential equations It is well known that

Ngày tải lên: 03/01/2018, 08:38

... descriptor form.Implicit Runge-Kutta methodsFormula of implicit Runge-Kutta methodsThe s-stage Runge-Kutta method for semi-explicit index 2 differential-algebraic equations (DAEs) is defined for a ... This modification allows for the extension of well-established high-order explicit Runge-Kutta methods for ordinary differential equations (ODEs) to half-explicit forms for differential-algebraic ... cᵢ] for each i, using the quadrature formula with weights aᵢ₁, , aᵢₛ.An RK method is said to have stage order q if C(q) is satisfied. s Implicit RK methods and half-explicit RK methods for semi-

Ngày tải lên: 23/12/2021, 21:29

... Semigroups Parabolic Equations V Implicit Evolution Equations Introduction Regular Equations Pseudoparabolic Equations Degenerate Equations Examples ... well-posed These include boundary value problems for (stationary) elliptic partial di erential equations and initial-boundary value problems for (time-dependent) equations of parabolic, hyperbolic, and ... Approximation of Evolution Equations Introduction Regular Equations Sobolev Equations Degenerate Equations Examples

Ngày tải lên: 31/03/2014, 15:56

... Methods for Ordinary Differential Equations, Second Edition J C Butcher © 2008 John Wiley & Sons, Ltd ISBN: 978-0-470-72335-7 454 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS ... accuracy of one-step methods for solving stiff systems of ordinary differential equations Math Comp., 28, 145 –162 Rattenbury N (2005) Almost Runge–Kutta methods for stiff and non-stiff ... (1965) Hybrid methods for initial value problems in ordinary differential equations SIAM J Numer Anal., 2, 69–86 456 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Gear

Ngày tải lên: 13/08/2014, 05:21

... problem,the strategy is to combine a method for solving equilibrium problems with a methodfor solving fixed point problems Most of the methods for solving equilibrium problems in the literature ... function f defined as 2.5.2 Solution methods for solving equilibrium problems For our purpose in the next chapters, we recall some well-known solution methodsfor equilibrium problems in this subsection ... for every y ∈ C (2.10)(see, for example, [28]) The hybrid projection method consists in combining the proximal point method forsolving equilibrium problems with the CQ projection method for solving

Ngày tải lên: 21/05/2016, 22:17

... consider system of equations and apply PDS algorithm to solving nonlinear Equations System 4 Nonlinear Equations System 4.1 The model of nonlinear equations system A general nonlinear equations system ... above for solving single-objective optimization problems In the experiment we transform nonlinear equations systems into single-objective optimization problems and apply PDS algorithm to solving ... technique for solving this multi-objective optimization problem It is to be noted that solutions found by this approach are Pareto optimal solutions Trang 84.3 PDS algorithm for solving Equations

Ngày tải lên: 04/09/2016, 09:08

... algorithms Iterative methods for solving monotone equilibrium problems 711 The rest of this paper is organized as follows In Sect we propose an algorithm (Algorithm 1) for solving strongly monotone ... and f1 is strongly monotone due to (iii) Iterative methods for solving monotone equilibrium problems 725 In order to implement Algorithm for solving (LEP), it remains to consider in detail two ... expanding scheme (11)–(12) algorithmically For simplicity of discussion, we assume that the constants τ and L are known in advance Otherwise, Iterative methods for solving monotone equilibrium problems

Ngày tải lên: 16/12/2017, 07:08

... numerical methods Two-point methods for solving coupled differential and algebraic equations are applied in Part while multipoint methods are applied in Part 2, and selected methods for solving ... integration methods: for ordinary differential equations, 25-30 for partial differential equations, 353-356 explicit methods, 353, 354 implicit methods, 355, 356 for stiff differential equations, ... substituting the expression for Cifor model I1 (Eq (11-28)) into Eq (14-104) is consistent with Gibbs' formula 14-3 Analogous to the expression for the volume of a liquid that forms a nonideal solution

Ngày tải lên: 23/05/2018, 09:01

... proposed methods are applied for locating bicycle stations in the city of Tabriz in Iran as a real case study The computational results of our study show that these methods can be implemented for ... deals with ambiguous and imprecise concepts, other methods have been developed for solving the facility location problems with uncertain parameters For instance, Küçükdeniz et al (2012) studied a ... unavailable and have uncertain properties Therefore, the assumption of uncertainty is needed for parameters of problem and to deal with this uncertainty, different methods like stochastic programming and

Ngày tải lên: 14/05/2020, 22:02

... following existence of the solutions for the integral equations: Theorem 3.2: If I1=∅, for any g1∈ R(K1), there exists a unique solution in L2[0, r0; r2] for the integral Equation (28) given by Trang ... K2areN(K1) = span {R n ; n ∈ I1} for I1 =∅; N(K1) = {0} for I1=∅, N(K2) = span {R n ; n ∈ I2} for I2 =∅; N(K2) = {0} for I2=∅, and the ranges of the operators K1and K2are Therefore, we have the following ... https://www.tandfonline.com/action/journalInformation?journalCode=gipe20Inverse Problems in Science and Engineering ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/gipe20 Three Landweber iterative methods for solving

Ngày tải lên: 28/04/2021, 13:40

... problems for singular in-tegral equations of the form (i)–(ii) By an algebraic method we reduce the problem (i)–(ii) to a system of linear algebraic equations which gives all solutions in a closed form ... for Singular Integral Equations 239 Trang 6Iþ KcR0 F1KcR0Xn1 k¼2 R1 .Rk1FkKk1KcR0 ! c ðtÞ ¼ gðtÞ; where gðtÞ ¼ I F1X n1 k¼2 R1 .Rk1FkKk1 ! Kcf1 ðtÞ: Rewrite this equation in the form ... Integral Equations 243 Trang 10By the same method as for the equation (12), every solution of this system canbe found in a closed form So every solution of the problem (5)–(6) is defined by the formula

Ngày tải lên: 19/10/2022, 18:31

... iterative methods for solving Sylvester equations of form solution, that is, Trang 2where λA and λB denote the spectra of A and B, respectively 6 In theory, the exactof linear equations of form ... iterative methods are becoming more and more popular Several iterative schemes for Sylvester equations have been proposed; see, for investigated for solving general coupled matrix equations and ... iterative methods can be derived by selecting two auxiliary matrices The selection of preconditioners is natural from the view point of splitting iteration methods for systems of linear equations

Ngày tải lên: 02/11/2022, 08:49

... Noor, “Resolvent methods for solving a system of variational inclusions,” International Journal of Modern Physics B In press 27 M A Noor and K I Noor, “Resolvent methods for solving the system ... 0, for all n ≥ satisfies some suitable conditions For suitable and appropriate choice of the operators T1 , T2 , A, g, h, g1 and spaces, one can obtain a wide class of iterative methods for solving ... the required result This equivalent formulation is used to suggest and analyze an iterative method for solving 2.1 To so, one rewrite 3.3 in the following form: x∗ − an x∗ y∗ an x∗ − g1 x∗ y...

Ngày tải lên: 21/06/2014, 06:20

... Preliminaries For solving the equilibrium problem for a bifunction F : C × C → R, let us assume that F satisfies the following conditions: A1 F x, x for all x ∈ C; A2 F is monotone, that is, F x, y A3 for ... for all x ∈ C, for a constant κ > 1; then, T is relaxed μ, ν -cocoercive and Lipschitz continuous Especially, T is ν-strong monotone Proof Since T x κx, for all x ∈ C, we have T : C → C For for ... method for solving the variational inequality 1.2 For a given u0 ∈ C, wn un PC un − λAun , PC wn − λAwn , n 0, 1, 2, , 1.7 which is also known as the modified double-projection method For the...

Ngày tải lên: 21/06/2014, 07:20

... various alternative numerical methods should be used for a specific problem, or even for a large class of problems 56 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Table 201(II) h π 200 ... ‘convergence’ In searching for other numerical methods that are suitable for solving initial value problems, attention is usually limited to convergent methods The reason for this is clear: a non-convergent ... function, y, on [x0 , x] by the formula y(x) = y(xk−1 ) + (x − xk−1 )f (xk−1 , y(xk−1 )), x ∈ (xk−1 , xk ], (210b) 66 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS for k = 1, 2, , n If we...

Ngày tải lên: 13/08/2014, 05:21

... diagrams) This effect persisted for a larger range of stepsizes for PEC methods than was the case for PECE methods NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 10−6 10−4 114 10−8 E 10−10 ... values for the Adams– Bashforth methods are given in Table 244(I) and for the Adams–Moulton methods in Table 244(II) The Adams methods are usually implemented in ‘predictor–corrector’ form That ... criteria to derive Adams–Bashforth methods with p = k for k = 2, 3, 4, and Adams–Moulton methods with p = k + for k = 1, 2, For k = 4, the Taylor expansion of (241c) takes the form hy (xn )(1 − β0 −...

Ngày tải lên: 13/08/2014, 05:21

... 124 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 262 Generalized linear multistep methods These methods, known also as hybrid methods or modified linear multistep methods, generalize ... Numerical Methods for Ordinary Differential Equations, Second Edition J C Butcher © 2008 John Wiley & Sons, Ltd ISBN: 978-0-470-72335-7 138 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS ... −1    1  0 1  2 1 1 6 3 126 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS The second order Adams–Bashforth and Adams–Moulton and PECE methods based on these are, respectively, ...

Ngày tải lên: 13/08/2014, 05:21