linear difference equations examples
báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot
... in Difference Equations Volume 2010, Article ID 594783, 19 pagesdoi:10.1155/2010/594783Research ArticleError Bounds for Asymptotic Solutions ofSecond-Order Linear Difference Equations II:The ... weconsider 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; itssolution takes the form of a particular solution added to an arbitrary linear combination ofsolutions to the associated homogeneous linear difference...
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Tài liệu 02 Ordinary Linear Differential and Difference Equations docx
... differential equations can be found in numerous texts onthe subject [1].2.2 Difference Equations Thedevelopmentofdifferenceequationsisparalleltothatofdifferentialequations. Weconsiderhereonly linear difference ... LLC2Ordinary Linear Differentialand Difference Equations B.P. LathiCalifornia State University, Sacramento2.1 Differential Equations Classical Solution•MethodofConvolution2.2 Difference Equations Initial ... concerning the classical method for solving differential equations alsoapply to difference equations. General discussion of difference equations can be found in texts onthe subject [2].References[1]...
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Tài liệu Đề tài " Isomonodromy transformations of linear systems of difference equations" pptx
... transformations of linear systems of difference equations By Alexei Borodin ISOMONODROMY TRANSFORMATIONS1147probability can be expressed through a solution of the difference Schlesinger equations ... the difference Schlesinger equations (3.1)–(3.3) with the initial conditions {Bi(0) = Bi}, and let Bi(x1, ,xn)bethesolution of the classical Schlesinger equations (5.4) with the initial ... of this conjecture, we explicitly show that the differenceSchlesinger equations converge to the conventional Schlesinger equations inthe limit ε → 0.Note that the monodromy representation of...
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báo cáo hóa học:" Research Article A Linear Difference Scheme for Dissipative Symmetric Regularized Long Wave Equations with Damping Term" doc
... 781750, 16 pagesdoi:10.1155/2010/781750Research ArticleA Linear Difference Scheme for DissipativeSymmetric Regularized Long Wave Equations withDamping TermJinsong Hu,1Youcai Xu,2and ... initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite differencescheme is designed. Existence ... Benjamin-Bona-Mahony equations, ” Journal ofMathematical 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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Tài liệu Solution of Linear Algebraic Equations part 1 docx
... overdetermined linear problem reduces toa (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 (AT· ... trade@cup.cam.ac.uk (outside North America).Chapter 2. Solution of Linear Algebraic Equations 2.0 IntroductionA set of linear algebraic equations looks like this:a11x1+ a12x2+ a13x3+ ···+a1NxN=b1a21x1+ ... linear combinations of each other, some of the equations may be so close to linearly dependent that roundoff errors in the machinerender them linearly dependent at some stage in the solution...
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
... about as efficient as anyother method. For solving sets of linear equations, Gauss-Jordan eliminationproduces both the solution of the equations for one or more right-hand side vectorsb, 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 andextend 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 wereplace any row in A by a linear combination of itself...
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Tài liệu Solution of Linear Algebraic Equations part 11 ppt
... not used for typical systems of linear equations. However, we willmeet special cases where QR is the method of choice.100Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL ... solve linear systems. In many applications only thepart (2.10.4) of the algorithm is needed, so we separate it off into its own routine rsolv.98Chapter 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 solveA · x = b (2.10.3)first form QT· b and then solveR · x = QT· b (2.10.4)by...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf
... 42Chapter 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 andone multiplication, are executed N3and N2M times (where there are N equations and M unknowns). The corresponding loops in Gaussian elimination are executedonly13N3times...
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Tài liệu Solution of Linear Algebraic Equations part 4 docx
... aij(2.3.10) Equations (2.3.8)–(2.3.10) total N2 equations for the N2+ N unknown α’s andβ’s (the diagonal being represented twice). Since the number of unknowns is greaterthan 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 Systemsof Equations The special case of a system of linear equations that is tridiagonal, that is, hasnonzero elements only on the...
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Tài liệu Solution of Linear Algebraic Equations part 5 docx
... 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 Systemsof Equations The special case of a system of linear equations that is tridiagonal, that is, hasnonzero elements only on the ... returned frombandec, and given a right-hand side vectorb[1 n], solves the band diagonal linear equations A · x = b. The solution vector x overwritesb[1 n]. The other input arrays are not...
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