Jacobi Approximations in Certain Hilbert Spaces and Their Applications to Singular Differential Equations

By B. Guo. 2000

144 citations recorded by the source corpus.

Subfields: Mathematical Physics, Mechanics of Materials, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/86b44187e6512c74851866976ade3e09a0f8834f

How researchers see this paper

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

In Mathematical Physics

1. Jie Shen
2. Lilian Wang
3. Yanping Chen
4. Yunxia Wei
5. B. Guo
6. Ali H. Bhrawy

In Mechanics of Materials

1. Jie Shen
2. Lilian Wang
3. Yanping Chen
4. Yunxia Wei
5. Zuliang Lu

In Numerical Analysis

1. Lilian Wang
2. Jie Shen
3. Yanping Chen
4. Yunxia Wei
5. B. Guo
6. Ali H. Bhrawy
7. Dumitru Băleanu
8. LM Assas

Citations in the corpus

• A Jacobi spectral Galerkin method for the integrated forms of fourth‐order elliptic differential equations (2009, unknown): “However, the general Jacobi approximations have been applied to some singular differential equations, see [15, 16].”
• Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions (2012, methodology): “Furthermore, we introduce the Jacobi polynomials (see also [13, 15]) J k (x) of indices α, β > −1 which are the solutions to singular Sturm-Liouville problems ( (1 − x)1+α(1 + x)1+β J′ k(x) )′ + k(k + α + β + 1)(1 − x)(1 + x) Jk(x) = 0.”
• Generalized Jacobi polynomials/functions and their applications (2009, background): “Guo [23,21,24] developed Jacobi approximations in certain Hilbert spaces with their applications to singular differential equations and some problems on infinite intervals.”
• Jacobi interpolation approximations and their applications to singular differential equations (2001, methodology): “Recently, Guo [21,22] developed Jacobi approximations in certain Hilbert spaces with their applications to singular differential equations.”
• On spectral approximations using modified Legendre rational functions: Application to the Korteweg-de Vries equation on the half line (2001, methodology): “…to reformulate the original problems in unbounded domains to singular/degenerate problems in bounded domains, and then use a suitable Jacobi approximation to treat the singular/degenerate problems [14, 17, 18]; another class of spectral methods is based on rational approximations, for…”