Integral equations and their applications /
M. Rahman.
- Boston : WITPress, c2007.
- 356 p. : ill. ; 23 cm.
1 Introduction 1.1 Preliminary concept of the integral equation 1.2 Historical background of the integral equation 1.3 An illustration from mechanics 1.4 Classification of integral equation 1.5 Converting IVP to volterra equations etc.
2 Volterra integral equations 2.1 Introduction 2.2 The methods of successive approximations 2.3 The methods of Laplace transform 2.4 The methods success composition substitutions 2.5 The A domain decomposition method etc.
3 Fredholm integral equations 3.1 Introduction 3.2 Various types of Fredholm integral equations 3.3 The methods of successive approximations: Neumann's series. 3.4 The method of successive substitutions 3.5 The A domain decomposition method etc.
4 Nonlinear integral equations 4.1 Introduction 4.2 The method of successive approximations 4.3 Picard's method of successive approximation 4.4 Existence theorem of Picard's method 4.5 The A domain decomposition method etc.
5 The singular integral equation 5.1 Introduction 5.2 Abel's problem 5.3 The generalized Abel's integral equation of the first kind 5.4 Abel's problem of the second kind integral equation 5.5 The weaky-singular volterra equation etc.
7 Symmetric kernels and orthogonal systems of functions 7.1 Development of green's function in one dimension 7.2 Green's function using the variation of parameters 7.3 Green's function in two dimensions 7.4 Green's function in three dimensions 7.5 Numerical formulation etc.