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### Rational Spectral Collocation Combined with the Singularity Separated Method for a System of Singularly Perturbed Boundary Value Problems

Lufeng Yang
2019 Mathematical Problems in Engineering
A novel rational spectral collocation method is presented combined with the singularity-separated technique for a system of singularly perturbed boundary value problems.  ...  The rational spectral collocation method in barycentric form with the sinh transformation is applied to solve the auxiliary third boundary problem.  ...  For reaction-diffusion, we solve auxiliary third boundary value problem (26) using a rational spectral collocation method with the sinh transformation.  ...

### Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems

Suqin Chen, Yingwei Wang, Xionghua Wu
2011 Journal of Computational Mathematics
A novel collocation method for a coupled system of singularly perturbed linear equations is presented.  ...  Here we present a kind of numerical method based on rational spectral collocation in barycentric form with sinh transform (RSC-sinh method) for solving a coupled system of singularly perturbed problems  ...  The authors are grateful to the referee and the editor for helpful comments and suggestions.  ...

### The Novel Rational Spectral Collocation Method for a Singularly Perturbed Reaction-Diffusion Problem with Nonsmooth Data

Lufeng Yang, Fotios Georgiades
2021 Mathematical Problems in Engineering
The rational spectral collocation method combined with a sinh transformation is applied to solve the weakened singularly boundary value problem.  ...  A novel rational spectral collocation combined with a singularity-separated method for this problem is presented.  ...  Y J Wu for his valuable suggestions and help for the work related to this paper. e work was partially supported by the Research Project of Science and Technology of Colleges and Universities in Ningxia  ...

### Page 4554 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews
Un- der suitable continuity and compatibility conditions on the data, a unique solution u(P,t) of (1) exists. For u < 1, problem (1) is singularly perturbed and has boundary layers near 0Q.  ...  The authors describe and analyze a finite element preconditioner for a system of linear algebraic equations that arise from a Cheby- shev spectral collocation discretization of a linear elliptic partial  ...

### A rational spectral collocation method for third-order singularly perturbed problems

Suqin Chen, Yingwei Wang
2016 Journal of Computational and Applied Mathematics
A new numerical method is developed for solving a class of third-order singularly perturbed boundary value problems.  ...  Then, the rational spectral collocation method in barycentric form with sinh transformation is applied to solve the system of ODEs.  ...  The authors also thank the anonymous referees and editors for helpful comments and suggestions which led to a significant improvement of the presentation.  ...

### Page 7625 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews
(IRL-CORK; Cork) A nonconforming finite element method for a singularly perturbed boundary value problem. (English and German summaries) Computing 54 (1995), no. 1, 1-25.  ...  Summary: “The paper is concerned with a singularly perturbed boundary value problem, having a single turning point.  ...

### Page 5662 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews
Summary: “We present a class of second-order optimal spline difference schemes derived from exponential cubic splines for a selfadjoint singularly perturbed 2-point boundary value problem.  ...  The collocation method devel- oped earlier by the authors for solving two-point boundary value problems [see Internat. J. Comput.  ...

### Page 1168 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews
Summary: “Boundary value problems for singularly perturbed semilinear elliptic equations are considered.  ...  FD method of arbitrary uniform order of accuracy for solving singularly perturbed boundary problems for second-order ordinary differential equations.  ...

### Page 6022 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews
A numerical method based on cubic splines with a nonuniform grid is given for singularly perturbed two-point boundary value problems having a turning point.  ...  Discretization of a singularly perturbed quasilinear boundary value problem on the unit interval using the standard three-point difference scheme is discussed.  ...

### Boundary Layer Resolving Pseudospectral Methods for Singular Perturbation Problems

Tao Tang, Manfred R. Trummer
1996 SIAM Journal on Scientific Computing
Pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary di erential equations which possess boundary layers.  ...  Stable and accurate results are obtained for very thin boundary layers with a fairly small number of spectral collocation points.  ...  Some recent work on spectral methods for boundary value problems is concerned with improving the condition numbers of the matrices for which linear systems have to be solved (e.g. 3, 5, 7] ).  ...

### Page 3341 of Mathematical Reviews Vol. , Issue 91F [page]

1991 Mathematical Reviews
Summary: “We present a numerical integration method for solv- ing linear, singularly perturbed two-point boundary value problems with a boundary layer on the left end of the underlying interval.  ...  65L10 Jacobs, S.J. (1-MI-OS) A pseudospectral method for two-point boundary value problems.  ...

### Page 410 of Mathematical Reviews Vol. , Issue 92a [page]

1992 Mathematical Reviews
The Galerkin method for singularly perturbed boundary value problems on adaptive nets. (Russian) Sibirsk. Mat. Zh. 31 (1990), no. 5, 138-148, 215; translation in Siberian Math.  ...  for linear boundary value problems.  ...

### Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations

Şuayip Yüzbaşı, Mehmet Sezer
2013 Abstract and Applied Analysis
By aid of the collocation points and the matrix operations, the suggested scheme converts singularly perturbed problem into a matrix equation, and this matrix equation corresponds to a system of linear  ...  This paper deals with the singularly perturbed delay differential equations under boundary conditions.  ...  The first author is supported by the Scientific Research Project Administration of Akdeniz University.  ...

### A point interpolation meshless method for the numerical solution of the singularly perturbed integral and integro-differential equations

N. S. M. Al-saif, E. A. Hussain
2013 International Journal of Mathematical Analysis
In this paper we propose a point interpolation mesh less method for solving singularly perturbed integro-differential integral equations.  ...  Recently, there has been an increasing interest in the study of singular and perturbed systems.  ...  Implicit Runge-Kutta methods were presented for singularly perturbed integro-differential-algebraic equations in [22] and for singular-ly perturbed integro-differential systems in [21] .  ...

### Page 5620 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews
Summary: “A combined finite difference method and local method of characteristic lines is presented for the numerical solution of singularly perturbed convection-diffusion problems.  ...  A note on iterative methods for solving singularly perturbed problems using non-monotone methods on Shishkin meshes. (English summary) Comput. Methods Appl. Mech.  ...
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