Handbook of Differential Equations, Volume 1Gulf Professional Publishing, 1998 - 801 pagine This book compiles the most widely applicable methods for solving and approximating differential equations. as well as numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.
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Sommario
A Definitions and Concepts 1 Definition of Terms | 1 |
Alternative Theorems | 13 |
Bifurcation Theory | 16 |
A Caveat for Partial Differential Equations | 24 |
Chaos in Dynamical Systems | 26 |
50 | 28 |
Classification of Partial Differential Equations | 33 |
Compatible Systems | 39 |
132 | 509 |
134 | 516 |
Monges Method | 522 |
138 | 528 |
Boundary Layer Method | 541 |
Functional Iteration | 542 |
Multiple Scales | 549 |
Regular Perturbation | 553 |
Conservation Laws | 43 |
Differential Resultants | 46 |
Existence and Uniqueness Theorems | 49 |
Fixed Point Existence Theorems | 54 |
HamiltonJacobi Theory | 56 |
Integrability of Systems | 60 |
43 | 62 |
Internet Resources | 66 |
Inverse Problems | 69 |
Limit Cycles | 72 |
Natural Boundary Conditions for a PDE | 76 |
NearIdentity Transformations | 78 |
Random Differential Equations | 83 |
SelfAdjoint Eigenfunction Problems | 86 |
Stability Theorems | 92 |
SturmLiouville Theory | 94 |
Classification of SturmLiouville Problems | 97 |
Variational Equations | 99 |
Well Posed Differential Equations | 104 |
Wronskians and Fundamental Solutions | 108 |
Zeros of Solutions | 111 |
I | 115 |
29 | 121 |
31 | 127 |
34 | 133 |
Transformation of an ODE to an Integral Equation | 143 |
Reduction of PDEs to a First Order System | 149 |
Transformations of Partial Differential Equations | 156 |
2 | 163 |
Finite Element Method | 174 |
51 | 175 |
Hybrid Computer Methods Invariant Imbedding | 176 |
Multigrid Methods | 177 |
5 | 188 |
II | 205 |
ComputerAided Solution | 218 |
Constant Coefficient Linear Equations | 225 |
55 | 236 |
58 | 243 |
Equidimensionalinx Equations | 250 |
61 | 256 |
64 | 263 |
67 | 272 |
69 | 279 |
71 | 285 |
73 | 297 |
75 | 303 |
77 | 309 |
79 | 319 |
80 | 326 |
83 | 344 |
85 | 352 |
88 | 360 |
91 | 370 |
96 | 381 |
Exact Methods for PDEs | 387 |
99 | 396 |
101 | 403 |
104 | 411 |
108 | 419 |
Separation of Variables | 443 |
114 | 450 |
Approximate Analytical Methods | 463 |
Equation Splitting | 471 |
The Phase Plane | 479 |
The Tangent Field | 485 |
Integral Methods | 493 |
129 | 499 |
Strained Coordinates 144 | 556 |
Picard Iteration | 560 |
Reversion Method | 562 |
Singular Solutions | 566 |
SolitonType Solutions | 567 |
Stochastic Limit Theorems | 569 |
Taylor Series Solutions | 572 |
Eigenvalue Approximation | 575 |
RayleighRitz | 578 |
WKB Method | 581 |
Concepts 154 Introduction to Numerical Methods | 587 |
Definition of Terms for Numerical Methods | 589 |
Integrating Stochastic Equations Symplectic Integration | 591 |
Available Software | 592 |
Rectilinear Grid 157 2 Two Dimensions Rectilinear Grid | 599 |
Irregular Grid | 601 |
Triangular Grid | 602 |
Ux | 605 |
184 | 606 |
Finite Difference Methodology | 607 |
159 | 611 |
and for polar coordinates | 612 |
Grid Generation Richardson Extrapolation | 615 |
ODE Approximations | 621 |
dependence | 624 |
Courant Criterion | 625 |
Von Neumann Test | 626 |
Testing Differential Equation Routines | 627 |
B Numerical Methods for ODEs 165 Analytic Continuation | 631 |
Box Method | 634 |
Shooting Method | 638 |
Continuation Method | 641 |
Continued Fractions | 644 |
Cosine Method | 647 |
Differential Algebraic Equations | 650 |
EigenvalueEigenfunction Problems | 657 |
Eulers Forward Method | 659 |
542 | 705 |
Use of Wavelets | 710 |
Weighted Residual Methods | 712 |
Numerical Methods for PDEs 186 Boundary Element Method | 717 |
549 | 721 |
Domain Decomposition 717 721 | 724 |
729 | |
733 | |
MonteCarlo Method | 737 |
739 | |
742 | |
Finite Differences 742 | 746 |
Lattice Gas Dynamics | 750 |
752 | |
756 | |
760 | |
765 | |
771 | |
780 | |
782 | |
783 | |
784 | |
785 | |
786 | |
789 | |
792 | |
793 | |
797 | |
798 | |
799 | |
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Abramowitz and Stegun algebraic analysis analytic Appl Applicable approximation arbitrary constant asymptotic bifurcation boundary conditions Boundary Value Problems Calogero and Degasperis coefficients Comput defined Degasperis 34 dependent variable derivative determine differential operator eigenfunctions eigenvalues elliptic equa exact solution finite given Green's function Hamiltonian Hence homogeneous initial conditions initial value problem integral interval inverse John Wiley limit cycle linear differential equation linear ordinary differential Lyapunov Lyapunov exponents Macsyma Math Mathematics matrix McGraw-Hill Book Company method Notes numerical obtain order ordinary differential ordinary differential equation Painlevé parabolic parameter partial differential equations Phys Physics polynomial Procedure satisfies self-adjoint SIAM singular solution to equation solve Springer-Verlag stable stochastic Sturm-Liouville Taylor series technique theorem tion transformation Unnamed equation vector Wiley & Sons Yields York zero ди მე მყ