Spectral and High-Order Methods with Applications

By Jie Shen, Tao Tang, Zhen-Huan Teng. 2006

482 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/469123e793ab6aa3da0b39456fea497a34304f12

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Yunxia Wei
2. Yongyong Cai
3. Yuwei Fan
4. Ishtiaq Ali
5. Hermann Brunner
6. Tao Wang
7. Ruo Li
8. XueSong Wang

Citations in the corpus

• A one-step optimal homotopy analysis method for nonlinear differential equations (2010, unknown): “First, consider a linear differential equation [15]: u00ðtÞ þ tu0ðtÞ uðtÞ 1⁄4 f ðtÞ; t 2 1⁄2 1;1 ; ð22Þ subject to the boundary conditions uð 1Þ 1⁄4 expð 5Þ þ sinð1Þ; uð1Þ 1⁄4 expð5Þ þ sinð1Þ; ð23Þ where f ðtÞ 1⁄4 ð24þ 5tÞ expð5tÞ þ ð2þ 2t(2)Þ cos t(2) ð4t(2) þ 1Þ sin t(2): ð24Þ The exact solution o”
• Globally Hyperbolic Regularization of Grad's Moment System (2011, background): “Since the Hermite polynomial HeM+1(x) has M+1 different zeros in R [17], all cj ’s are distinct.”
• A SPECTRAL METHOD FOR PANTOGRAPH-TYPE DELAY DIFFERENTIAL EQUATIONS AND ITS CONVERGENCE ANALYSIS * (2009, background): “, [6, 12]) which yields wk,j = 1 qN(N + 1)[LN(xk)](2) N”
• Mathematical Models and Numerical Methods for Bose-Einstein Condensation (2012, methodology): “72) will be discretized in space by sine pseudospectral method [23,47,164,165] and the linear ODE (8.”
• Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions (2012, methodology): “AMS subject classifications: 45J05, 65R20 Key words: Volterra integro-differential equations, weakly singular kernels, spectral methods, convergence analysis.”
• Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed (2010, unknown): “[2, 10].”
• Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind (2012, unknown): “, [5,20].”
• Jacobi spectral solution for integral algebraic equations of index-2 (2011, unknown): “[19])”
• A NOTE ON JACOBI SPECTRAL-COLLOCATION METHODS FOR WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS WITH SMOOTH SOLUTIONS * (2013, unknown): “As defined in [2,7,16], the set of Jacobi polynomials {J n (x)} ∞ n=0 forms a complete L 2 ωα,β(−1, 1)orthogonal system, where L2ωα,β(−1, 1) is a weighted space defined by L2ωα,β(−1, 1) = {v : v is measurable and ||v||ωα,β < ∞} , equipped with the norm”
• An improved Levin quadrature method for highly oscillatory integrals (2010, methodology): “The Chebyshev differentiation matrix [1,2,5,22,24], which is a powerful tool in the Chebyshev pseudo-spectral method, is employed to solve the ODE (2).”