linear difference equations wikipedia

... in Difference Equations Volume 2010, Article ID 594783, 19 pages doi:10.1155/2010/594783 Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The ... we consider a nonlinear first-order difference equation. 2 Advances in Difference Equations Unlike t he method used by Olver 4 to treat asymptotic solutions of second-order linear differential equations, ... second-order linear difference equation; its solution takes the form of a particular solution added to an arbitrary linear combination of solutions to the associated homogeneous linear difference...

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... differential equations can be found in numerous texts on the subject [1]. 2.2 Difference Equations Thedevelopmentofdifferenceequationsisparalleltothatofdifferentialequations. Weconsiderhere only linear difference ... LLC 2 Ordinary Linear Differential and Difference Equations B.P. Lathi California State University, Sacramento 2.1 Differential Equations Classical Solution • MethodofConvolution 2.2 Difference Equations Initial ... concerning the classical method for solving differential equations also apply to difference equations. General discussion of difference equations can be found in texts on the subject [2]. References [1]...

Ngày tải lên: 27/01/2014, 03:20

... transformations of linear systems of difference equations By Alexei Borodin ISOMONODROMY TRANSFORMATIONS 1147 probability can be expressed through a solution of the difference Schlesinger equations ... the difference Schlesinger equations (3.1)– (3.3) with the initial conditions {B i (0) = B i }, and let B i (x 1 , ,x n )bethe solution of the classical Schlesinger equations (5.4) with the initial ... of this conjecture, we explicitly show that the difference Schlesinger equations converge to the conventional Schlesinger equations in the limit ε → 0. Note that the monodromy representation of...

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... 781750, 16 pages doi:10.1155/2010/781750 Research Article A Linear Difference Scheme for Dissipative Symmetric Regularized Long Wave Equations with Damping Term Jinsong Hu, 1 Youcai Xu, 2 and ... initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence ... Benjamin-Bona-Mahony equations, ” Journal of Mathematical Analysis and Applications, vol. 141, no. 2, pp. 527–537, 1989. 3 C. J. Amick, J. L. Bona, and M. E. Schonbek, “Decay of solutions of some nonlinear...

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... overdetermined linear problem reduces to a (usually) solvable linear problem, called the • Linear least-squares problem. Thereduced set of equationsto be solved can bewritten as the N ×N set of equations (A T · ... trade@cup.cam.ac.uk (outside North America). Chapter 2. Solution of Linear Algebraic Equations 2.0 Introduction A set of linear algebraic equations looks like this: a 11 x 1 + a 12 x 2 + a 13 x 3 + ···+a 1N x N =b 1 a 21 x 1 + ... linear combinations of each other, some of the equations may be so close to linearly dependent that roundoff errors in the machine render them linearly dependent at some stage in the solution...

Ngày tải lên: 15/12/2013, 04:15

... about as efficient as any other method. For solving sets of linear equations, Gauss-Jordan elimination produces both the solution of the equations for one or more right-hand side vectors b, and ... writeout equations only for the case of four equations and four unknowns, and with three different right- hand side vectors that are known in advance. You can write bigger matrices and extend the equations ... to writing the same set of linear equations in a different order. • Likewise, the solution set is unchanged and in no way scrambled if we replace any row in A by a linear combination of itself...

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... not used for typical systems of linear equations. However, we will meet special cases where QR is the method of choice. 100 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL ... solve linear systems. In many applications only the part (2.10.4) of the algorithm is needed, so we separate it off into its own routine rsolv. 98 Chapter 2. Solution of Linear Algebraic Equations Sample ... factorizations we have met (LU, SVD, Cholesky), QR decompo- sition can be used to solve systems of linear equations. To solve A · x = b (2.10.3) first form Q T · b and then solve R · x = Q T · b (2.10.4) by...

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... 42 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... Program B-2, p. 298. Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley). Ralston, A., and Rabinowitz, P. 1978, A First Course in Numerical ... containing one subtraction and one multiplication, are executed N 3 and N 2 M times (where there are N equations and M unknowns). The corresponding loops in Gaussian elimination are executed only 1 3 N 3 times...

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... a ij (2.3.10) Equations (2.3.8)–(2.3.10) total N 2 equations for the N 2 + N unknown α’s and β’s (the diagonal being represented twice). Since the number of unknowns is greater than the number of equations, ... Solution of Linear Algebraic Systems (Engle- wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18. Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New ... Cambridge University Press). 2.4 Tridiagonal and Band Diagonal Systems of Equations The special case of a system of linear equations that is tridiagonal, that is, has nonzero elements only on the...

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... Solution of Linear Algebraic Systems (Engle- wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18. Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New ... Cambridge University Press). 2.4 Tridiagonal and Band Diagonal Systems of Equations The special case of a system of linear equations that is tridiagonal, that is, has nonzero elements only on the ... returned from bandec , and given a right-hand side vector b[1 n] , solves the band diagonal linear equations A · x = b. The solution vector x overwrites b[1 n] . The other input arrays are not...

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