1549301742-The_Theory_of_Difference_Schemes__Samarskii

xvi Contents

3.2 Conservative schemes 147

3.3 Convergence and accuracy of homogeneous conservative

schemes 159

3.4 Hornogeneous difference sclten1es on non-equidistant grids 168

3.5 Other problems 178

3.6 Difference Green's function 199

3.7 Higher-accuracy sche1nes 207

3.8 l\IIetltods for designing difference schemes 214

3.9 Stability with respect to coefficients 229

4 Difference schen1es for elliptic equations^237

4.1 The Dirichlet difference problen1 for Poisson's equation 237

4.2 The maximmn principle 258

4.3 Stability and convergence of the Dirichlet difference problem 265

4.4 Some properties of difference elliptic operators^272

4.5 Higher-accuracy sche1nes for Poisson's equation 290

5 Difference schemes for time-dependent equations

with constant coefficients 299

5.1 One-dimensional heat conduction equation with constant

coefficients 299

5.2 Asy1nptotic stability :327

5.3 Schen1es for the heat conduct.ion equation with several

spatial variables 340

5 .4 Schrodinger tin1e-clepenclent equation 349

5.5 The transfer equation 354

5.6 Difference schen1es for the equation of vibrations of a string 364

5. 7 Selected problen1s 378

6 Stability theory of difference schen:1es

6.1 Operator-difference schemes

6.2 Classes of stable two-layer schemes

383

383

397