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Inhaltsangabe
1 Direct Methods for Solving Difference Equations.- 1.1 Grid equations. Basic concepts.- 1.2 The general theory of linear difference equations.- 1.3 The solution of linear equations with constant coefficients.- 1.4 Second-order equations with constant coefficients.- 1.5 Eigenvalue difference problems.- 2 The Elimination Method.- 2.1 The elimination method for three-point equations.- 2.2 Variants of the elimination method.- 2.3 The elimination method for five-point equations.- 2.4 The block-elimination method.- 3 The Cyclic Reduction Method.- 3.1 Boundary-value problems for three-point vector equations.- 3.2 The cylic reduction method for a boundary-value problem of the first kind.- 3.3 Sample applications of the method.- 3.4 The cyclic reduction method for other boundary-value problems.- 4 The Separation of Variables Method.- 4.1 The algorithm for the discrete Fourier transform.- 4.2 The solution of difference problems by the Fourier method.- 4.3 The method of incomplete reduction.- 4.4 The staircase algorithm and the reduction method for solving tridiagonal systems of equations.
1 Direct Methods for Solving Difference Equations.- 1.1 Grid equations. Basic concepts.- 1.2 The general theory of linear difference equations.- 1.3 The solution of linear equations with constant coefficients.- 1.4 Second-order equations with constant coefficients.- 1.5 Eigenvalue difference problems.- 2 The Elimination Method.- 2.1 The elimination method for three-point equations.- 2.2 Variants of the elimination method.- 2.3 The elimination method for five-point equations.- 2.4 The block-elimination method.- 3 The Cyclic Reduction Method.- 3.1 Boundary-value problems for three-point vector equations.- 3.2 The cylic reduction method for a boundary-value problem of the first kind.- 3.3 Sample applications of the method.- 3.4 The cyclic reduction method for other boundary-value problems.- 4 The Separation of Variables Method.- 4.1 The algorithm for the discrete Fourier transform.- 4.2 The solution of difference problems by the Fourier method.- 4.3 The method of incomplete reduction.- 4.4 The staircase algorithm and the reduction method for solving tridiagonal systems of equations.
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