Griffiths' Formalism on the Calculus of Variations

Chapters in this book

1. Frontmatter I
2. CONTENTS V
3. Preface IX
4. Generating Optimal Runge-Kutta Methods 1
5. Minimization Techniques in Neutral Network Supervised Training 9
6. An Extended Marquardt-Levenberg Method for Function Minimization 17
7. Approximate Iterative Method for a System of Nonlocal Parabolic Functional-Differential Problems 25
8. On a Delay Logistic Equation with Nonlinear Average Growth Rate 35
9. Griffiths' Formalism on the Calculus of Variations 45
10. A Nonlinear Elliptic Equation with Nonlinearity Crossing Eigenvalues 53
11. The Partial Differential Equation Associated to the Generalized Kac-Feynman Integral Equation 61
12. A primal-dual method for discrete l_p approximation 69
13. Utilizing Curvature Information in Multi-step Quasi-Newton methods for Optimization 79
14. Utilizing Curvature Information in Multi-Step Quasi-Newton Methods for Optimization 87
15. On Numerical Results for the Generalized Curve Shortening Equations 95
16. Analytic continuation of holomorphic solutions of partial differential equations 103
17. The Condition (S) of Kawai, the Property of Completely Regular Growth and the Estimate of the Micro-Support of the Complex of a Convolution Operator 111
18. One Approach to Exact Solutions of a piecewise Linear Differential Equation 119
19. Numerical integration of irregularly oscillating functions by parameter-dependent compound quadrature formulae 127
20. Initial Value Problem for Abstract Differential Equations of Sobolev Type 135
21. A parallel approach to bivariate splines 143
22. Recent results on Liénard systems 151
23. Extension of Holomorphic Mappings in Infinite Dimension 159
24. Numerical approximations to some nonlinear diffusion equation with strong absorption 165
25. On the Initial Boundary Value Problem for the Linearized MHD Equation 173
26. Modified Gompertz Curve and it's Applications I 181
27. An Experimental Algorithm for Ending Eigenvalues 189
28. On a Degenerate Boundary Value Problem for Second Order Quasilinear Elliptic Operators 197
29. Some Improperly Posed Problems and their Nonlocal Regularization 209
30. Methods for the Computation of Periodic Solutions of Dynamical Systems 213
31. The Computation of Equilibrium Points of Up-to-Three Dimensional Dynamical Systems Using the Topological Degree Theory 221
32. The boundary behavior of a bounded function 229
33. Application of Statistical Moments on Exterior Dirichlet Problem 235
34. Discrete Trigonometric Methods for Boundary Integral Equations in Hòlder-Zygmund Spaces 241
35. On the conditioning and the solution, by means of multigrid methods, of symmetric (block) Toeplitz linear systems 249
36. Differential Game Theory at Control System design for a Manipulator 257
37. Two-Point Formulas in Hermite-Birkhoff Quadratures 265
38. Numerical Direct Methods for Initial Value Problems of Any r-th-Order Ordinary Differential Equations 273
39. A Stochastic Compartmental Model for Dynamic Biological Systems 281
40. Round-Off Error of Numerical Integral by a Finite Chebyshev Series in a Floating-Point Number System 289
41. Floating-Point Number Solutions in a Simple Linear Equation with Multiplication Algorithm 297
42. Multi-Peak System Identification with Gauss-Weierstrass Transform 305
43. Continuation of bounded holomorphic functions from one-codimensional subspace to pseudoconvex domains 313
44. Singularities of surfaces defined by Monge-Ampere equations of hyperbolic type 321
45. De Rham Cohomology of Toroidal Groups and Complex Line Bundles 329
46. Generalized Bisection Methods for Imprecise Problems 337
47. Periodic Orbits and Invariant Surfaces of Nonlinear Mappings 345
48. Expected Behavior of Bisection Based Methods for Counting and Computing All the Roots of a Function 353
49. Approximate Lie Symmetries for Diffusion Equations with Non-linear Perturbations 361
50. On the Stability of a Multistep Method 369
51. Numerical Treatment of Mathematical Models for Infectious Diseases 377
52. Applications of the Beltrami Function in the Physics of Plasmas 387
53. Necessary and sufficient conditions for Fredholmness of irregular singular partial differential operators 401
54. On the Computation of Zeros of Bessel and Bessel-Related Functions 409
55. Linearized Viscoelastic Wave Propagation 417