Integral equations and their applications /
Rahman, M.
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.
6 Integro-differential equations
6.1 Introduction
6.2 Volterra integro-differential equations
6.3 Fredholm integro-differential equations
6.4 The Laplace transform method
6.5 Exercises
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.
8 Application
8.1 Introduction
8.2 Ocean waves
8.3 Nonlinear wave-wave interactions
8.4 Picard's method of successive approximation
8.5 Adomian decomposition method
etc.
Includes bibliographical references . _ Subject Index : p. 355 - 356
9781845641016 (hbk.) 1845641019 (hbk.)
2007922339
GBA726627 bnb
013709564 Uk
Integral equations.
515.45 / RAH.
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.
6 Integro-differential equations
6.1 Introduction
6.2 Volterra integro-differential equations
6.3 Fredholm integro-differential equations
6.4 The Laplace transform method
6.5 Exercises
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.
8 Application
8.1 Introduction
8.2 Ocean waves
8.3 Nonlinear wave-wave interactions
8.4 Picard's method of successive approximation
8.5 Adomian decomposition method
etc.
Includes bibliographical references . _ Subject Index : p. 355 - 356
9781845641016 (hbk.) 1845641019 (hbk.)
2007922339
GBA726627 bnb
013709564 Uk
Integral equations.
515.45 / RAH.