Applied Singular Integral Equations

Contents......Page 8
Preface......Page 6
1.1 Basic Definitions......Page 11
1.2.1 Weakly singular integral equation (Abel’s problem)......Page 17
1.2.2 Cauchy type singular integral equations......Page 19
1.2.3 Hypersingular integral equation......Page 28
2.1 Abel integral equation and its generalization......Page 30
2.2 Integral equations with logarithmic type of singularities......Page 36
2.3 Integral equations with Cauchy type kernels......Page 39
2.4 Application to boundary value problems in elasticity and fl uid mechanics......Page 55
3.1 Cauchy principal value integrals......Page 57
3.2 Some basic results in complex variable theory......Page 59
3.3 Solution of singular integral equations involving closed contours......Page 64
3.4 Riemann Hilbert problems......Page 65
3.5 Generalised Abel integral equations......Page 72
3.6 Singular integral equations with logarithmic kernels......Page 78
3.7 Singular integral equation with logarithmic kernel in disjoint intervals......Page 89
4.1 Integral equations with logarithmically singular kernels......Page 94
4.2 Integral equations with Cauchy type kernels......Page 106
4.3 Use of Poincare'-Bertrand formula......Page 109
4.4 Solution of singular integral equation involving two intervals......Page 114
5.1 Definitions......Page 121
5.2 Occurrence of hypersingular integral equations......Page 125
5.3 Solution of simple hypersingular integral equation......Page 136
5.4 Solution of hypersingular integral equation of the second kind......Page 148
6.1 A class of singular integro-differential equations......Page 152
6.2 A special type of singular integro-differential equation......Page 160
6.3 Numerical solution of a special singular integro-differential equation......Page 165
6.4 Approximate method based on polynomial approximation......Page 180
6.5 Approximate method based on Bernstein polynomial basis......Page 184
7.1 Galerkin method......Page 190
7.2 Use of single-term Galerkin approximation......Page 194
7.3 Galerkin method for singular integral equations......Page 199
8.1 The general numerical procedure for Cauchy singular integral equation......Page 202
8.2 A special numerical technique to solve singular integrals equations of first kind with Cauchy kernel......Page 208
8.3 Numerical solution of hypersingular integral equation using simple polynomial expansion......Page 217
8.4 Numerical solution of simple hypersingular integral equation using Bernstein polynomials as basis......Page 223
8.5 Numerical solution of some classes of logarithmically  singular integral equations using Bernstein polynomials......Page 226
8.6 Numerical solution of an integral equation of some special type......Page 234
8.7 Numerical solution of a system of generalized Abel integral equations......Page 241
9. Some Special Types of Coupled Singular Integral Equations of Carleman Type and their Solutions......Page 250
9.1 The Carleman singular integral equation......Page 251
9.2 Solution of the coupled integral equations for large l......Page 252
9.3 Solution of the coupled integral equations for any l......Page 255
Bibliography......Page 267