Advanced Numerical and Semi-Analytical Methods for Differential Equations

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, ...