Numerical solution of partial differential equations in science and engineering

Preface......Page 6
Contents......Page 8
1.0 NOTATION......Page 16
1.1 FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS......Page 19
1.2 SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS......Page 27
1.3 SYSTEMS OF FIRST-ORDER PDEs......Page 36
1.4 INITIAL AND BOUNDARY CONDITIONS......Page 43
REFERENCES......Page 48
2.1 FINITE DIFFERENCE APPROXIMATIONS......Page 49
2.2 INTRODUCTION TO FINITE ELEMENTAPPROXIMATIONS......Page 64
2.3 RELATIONSHIP BETWEEN FINITE ELEMENT ANDFINITE DIFFERENCE METHODS......Page 119
REFERENCES......Page 122
3.1 TRIANGULAR ELEMENTS......Page 124
3.3 BOUNDARY CONDITIONS......Page 152
3.4 THREE-DIMENSIONAL ELEMENTS......Page 156
REFERENCES......Page 163
4.1 PARTIAL DIFFERENTIAL EQUATIONS......Page 164
4.2 MODEL DIFFERENCE APPROXIMATIONS......Page 166
43 DERIVATION OF FINITE DIFFERENCEAPPROXIMATIONS......Page 168
4.4 CONSISTENCY AND CONVERGENCE......Page 177
4.5 STABILITY......Page 181
4.6 SOME EXTENSIONS......Page 201
4.7 SOLUTION OF FINITE DIFFERENCE APPROXIMATIONS......Page 228
4.8 COMPOSITE SOLUTIONS......Page 234
4.9 FINITE DIFFERENCE APPROXIMATIONS IN TWO SPACEDIMENSIONS......Page 249
4.10 THREE-DIMENSIONAL PROBLEMS......Page 280
4.11 FINITE ELEMENT SOLUTION OF PARABOLIC PARTIALDIFFERENTIAL EQUATIONS......Page 291
4.12 FINITE ELEMENT APPROXIMATIONS IN ONE SPACEDIMENSION......Page 300
4.13 FINITE ELEMENT APPROXIMATIONS IN TWO SPACEDIMENSIONS......Page 324
4.14 FINITE ELEMENT APPROXIMATIONS IN THREE SPACEDIMENSIONS......Page 363
4.15 SUMMARY......Page 365
REFERENCES......Page 366
5.1 MODEL ELLIPTIC PDEs......Page 370
5.2 FINITE DIFFERENCE SOLUTIONS IN TWO SPACEDIMENSIONS......Page 375
5.3 FINITE DIFFERENCE SOLUTIONS......Page 449
5.4 FINITE ELEMENT METHODS FOR TWO SPACEDIMENSIONS......Page 456
\r5.5 BOUNDARY INTEGRAL EQUATION METHODS......Page 476
5.6 THREE-DIMENSIONAL FINITE ELEMENT SIMULATION......Page 496
REFERENCES......Page 497
6.0 INTRODUCTION......Page 501
6.1 EQUATIONS OF HYPERBOLIC TYPE......Page 502
6.2 FINITE DIFFERENCE SOLUTION OF FIRST-ORDERSCALAR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS......Page 504
6.3 FINITE DIFFERENCE SOLUTION OF FIRST-ORDERVECTOR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS......Page 541
6.4 FINITE DIFFERENCE SOLUTION OF FIRST-ORDERVECTOR CONSERVATIVE HYPERBOLIC PARTIALDIFFERENTIAL EQUATIONS......Page 543
6.5 FINITE DIFFERENCE SOLUTIONS TO TWO- ANDTHREE-DIMENSIONAL HYPERBOLIC PARTIALDIFFERENTIAL EQUATIONS......Page 554
6.6 FINITE DIFFERENCE SOLUTION OF SECOND-ORDERMODEL HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS......Page 577
6.7 FINITE ELEMENT SOLUTION OF FIRST-ORDER MODELHYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS......Page 604
6.8 FINITE ELEMENT SOLUTION OF TWO- ANDTHREE-SPACE-DIMENSIONAL FIRST-ORDER HYPERBOLICPARTIAL DIFFERENTIAL EQUATIONS......Page 635
6.9 FINITE ELEMENT SOLUTION OF FIRST-ORDER VECTORHYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS......Page 640
6.10 FINITE ELEMENT SOLUTION OF TWO- ANDTHREE-SPACE-DIMENSIONAL FIRST-ORDER VECTORHYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS......Page 660
6.11 FINITE ELEMENT SOLUTION OFONE-SPACE-DIMENSIONAL SECOND-ORDER HYPERBOLICPARTIAL DIFFERENTIAL EQUATIONS......Page 670
6.12 FINITE ELEMENT SOLUTION OF TWO- ANDTHREE-SPACE-DIMENSIONAL SECOND-ORDERHYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS......Page 680
REFERENCES......Page 682
Index......Page 686