1549301742-The_Theory_of_Difference_Schemes__Samarskii

Contents xvii

6.3 Classes of stable three-layer schemes 428

7 Ho111ogeneous difference sche111es for tin1e-dependent

equations of inathematical physics 459

7 .1 Homogeneous difference schernes for the heat conduction

equation with variable coefficients 459

7.2 Homogeneous difference schemes for hyperbolic equations 499

8 Difference n1ethods for solving nonlinear equations

of n1athe111atical physics 507

8.1 Difference methods for solving the quasilinear heat

conduction equation 507

c. R '2 Conservative difference schemes of nonstationary

gas dynamics 525

9 Econo111ical difference schenres for 111ultidi111ensional

problems in 111athen1atical physics 543

9.1 The alternating direction method (the longitudinal-transverse

scheme) for the heat conduction equation

9.2 Economical factorized schemes

9.3 The smnmarized approxin1ation method

10 Methods for solving grid equations

10.1 Direct methods

10 .2 Two-layer iteration schemes

10.3 The alternative-triangular rnethod

10.4 Iterative alternating direction methods

10.5 Other iterative 1nethocls

Sy111bols

Concluding re111arks

References

Index

543

564

591

643

643

653

676

710

729

745

749

753

759