Index
- a
- Adams‐Bashforth method 10
- Adams‐Moulton method 10, 11, 16
- Addition and Subtraction of Intervals 202, 206
- Adjoint operator 92
- Adomian decomposition method (ADM) 103, 119, 124, 126–128, 157, 177
- Adomian polynomials 120–127, 182, 183, 185
- Advection equation 134, 136, 154, 161, 179, 181
- Akbari‐Ganji's method (AGM) 103, 104, 106, 107, 109, 111, 157
- α‐Cut of TFN 209
- b
- Backward Difference Scheme 54, 55
- Boundary characteristic orthogonal polynomials (BCOPs) 31, 40, 45–51
- Boundary Element Method (BEM) 91–97
- Boundary integral equation (BIE) 93, 96–99
- Boundary point 96–99
- Boundary value problem (BVP) 2, 31, 33, 36, 37, 40, 45–48, 49, 60, 69, 75, 91, 93, 119
- Burger's equation 115, 136, 181, 182
- c
- Cahn–Allen equation 115
- Canonical form 124
- Cell faces 88
- Central Difference Scheme 54, 55, 57, 88
- Chebyshev polynomials 157
- Collocation method 33, 41
- Conservation laws 82
- Conservation property 81
- Control volume domain 82
- Convection–diffusion 82, 83, 84, 87
- Convergence 53, 119, 121, 132, 149
- Convolution 26, 27
- Correction functional 141–143, 145
- Crisp 203–212, 217, 221–223, 226
- d
- Daubechies wavelet 167
- Deformation 132, 150, 151, 154, 155
- Differential Form 199
- Differential Quadrature 157
- Diffusion equation 57, 71, 74, 84, 86, 100
- Dirac Delta Function 33, 93, 94, 97
- Dirichlet boundary conditions 97, 99, 192
- Discrete grid points 53, 54
- Discretization Techniques 81, 82
- Duffing equation 105, 107, 108
- Dynamic analysis 76, 78, 218, 223, 225
- f
- Finite Difference Method 53, 81, 157
- Finite Difference Schemes 53, 54, 55, 58
- Finite element method (FEM) 31, 63, 64, 65, 75, 78, 81, 157, 217, 218
- Finite elements 63, 219, 223
- Finite volume method 81, 82, 157
- Forced nonlinear differential equations 103, 105, 107
- Forward Difference Scheme 54, 57
- Fourier transform 2, 19, 25, 26, 28
- Fractal differential equations 189–191, 194
- Fractal geometry 189, 190
- Functional 48, 49, 50, 157
- Fundamental Solution 92–98
- Fuzzy initial conditions 209–212
- Fuzzy Linear System of Differential Equations (FLSDE) 209, 210, 211, 213
- Fuzzy set theory 197, 209, 217
- Fuzzy Uncertainty 209, 211
- g
- Galerkin FEM 63, 71, 75, 219
- Galerkin method 31, 39–42, 46, 65–67, 69, 71, 72, 75, 217, 219
- Gauss‐divergence theorem 83
- Geometrical representation 3, 213
- Gradient 85
- Gram–Schmidt Orthogonalization Process 45
- Green–Gauss theorem 96
- Green's Function 93, 95
- Green's integral formula 95
- Green's integral theorems 92, 93
- Grid generation 84
- h
- Haar wavelet 167–170, 172, 175
- Haar wavelet–collocation method 173, 174
- Heat equation 27, 56, 58, 74, 191, 192, 194
- Heaviside Function 93
- Helmholtz equation 106
- He's polynomials 178, 180, 182
- Heun's method 6
- Homogeneous terms 127
- Homotopic 132
- Homotopy analysis method (HAM) 103, 131, 149, 151, 153, 157
- Homotopy perturbation method (HPM) 103, 131, 133, 134, 136, 138, 149, 157, 177
- Homotopy Perturbation Transform Method 177
- Hukuhara Differentiability 198, 199
- Hybrid methods 177, 186
- Hyperbolic nonlinear problem 126
- i
- Implicit finite difference scheme 55, 57, 58
- Improved Euler method 5–9
- Infinite series 120, 121, 125, 127
- Initial value problems (IVPs) 2, 9, 14, 20, 119, 121
- Integral form 82, 83, 84, 92, 95, 199
- Integral kernel 95
- Integral operators 92
- Integral transform 19, 20, 25
- Integro‐differential equations‐103 141
- Interval analysis 197, 198, 217, 218
- Interval Arithmetic 198, 217, 218, 221
- Interval differential equations (IDEs) 197, 198, 218, 213, 221, 223, 225
- Interval eigenvalue problem 218, 226, 227
- Interval finite element method (IFEM) 218, 224,
- Interval Galerkin finite element method (IGFEM) 217–219, 221
- Interval initial conditions 202
- Interval system of equations 218, 220, 222, 224
- Interval system of linear equations 218, 223
- Interval Uncertainty 197, 217, 218, 221
- Interval‐valued functions 198
- Inverse Laplacian operator 20
- Inverse linear operator 124
- Invertible operator 119
- k
- Koch curve 190
- l
- Lagrange multiplier 142, 144, 145
- Laplace Adomian decomposition method 177, 182
- Laplace equation 60, 94, 96
- Laplace transform 19, 20, 109, 177
- Laplacian operator 19, 20, 94
- Least‐square method 31, 33, 37, 40, 41, 42
- Legendre polynomials 157, 158
- Linear Differential Operator 32, 92, 152, 178
- Linear interpolation 85
- Linear property 20
- Lower and upper bounds 198, 202, 218, 227
- Lower‐bound solution 204
- o
- Orthogonal functions 45
- s
- Self‐adjoint property 92
- Shape function 31, 32, 64, 66, 67, 72, 219
- Shifted Legendre polynomials 158
- Sierpinski gasket (SG) 190–192, 194
- Snowflakes 190
- Stability conditions 58
- Static analysis 76, 218, 223
- Steady‐state 84
- Subdomain method 35, 36, 41
- Successive approximations 141, 142, 144, 145, 179, 185
- System of equations 35, 36, 39, 45, 49, 60, 65, 68–70, 73, 74, 76, 77, 114, 117, 124, 125, 173, 217, 218, 220, 222, 224
- System of ODEs 13, 16, 123, 159, 161, 162
- System of PDEs 127, 128
- z
- Zero‐order deformation 150
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.