scholarly journals A collocation method of matched eigenfunction expansions on the boundary-value problem of wave-structure interactions.

1990 ◽  
pp. 265-274
Author(s):  
Akinori YOSHIDA ◽  
Haruyuki KOJIMA ◽  
Yoshihiro TSURUMOTO
Keyword(s):  
Boundary Value Problem ◽  
Collocation Method ◽  
Boundary Value ◽  
Wave Structure ◽  
Eigenfunction Expansions ◽  
Matched Eigenfunction Expansions

scholarly journals Subdivision Collocation Method for One-Dimensional Bratu’s Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ghulam Mustafa ◽  
Syeda Tehmina Ejaz ◽  
Sabila Kouser ◽  
Shafqat Ali ◽  
Muhammad Aslam
Keyword(s):  
Boundary Value Problem ◽  
Collocation Method ◽  
Boundary Value ◽  
Accurate Solution ◽  
Subdivision Scheme ◽  
Algebraic Equations ◽  
Physical Sciences ◽  
One Dimensional ◽  
Bratu’S Problem ◽  
Approximating Subdivision Scheme

The purpose of this article is to employ the subdivision collocation method to resolve Bratu’s boundary value problem by using approximating subdivision scheme. The main purpose of this researcher is to explore the application of subdivision schemes in the field of physical sciences. Our approach converts the problem into a set of algebraic equations. Numerical approximations of the solution of the problem and absolute errors are compared with existing methods. The comparison shows that the proposed method gives a more accurate solution than the existing methods.

scholarly journals A Barycentric Interpolation Collocation Method for Linear Nonlocal Boundary Value Problems

2016 ◽  
Vol 10 (11) ◽  
pp. 140
Author(s):  
Dan Tian ◽  
Weiya Li ◽  
Cec Yulan Wang
Keyword(s):  
Boundary Value Problem ◽  
Collocation Method ◽  
Present Method ◽  
Lagrange Interpolation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Higher Order ◽  
Point Boundary ◽  
Numerical Treatment ◽  
Barycentric Interpolation

This paper is devoted to the numerical treatment of a class of higher-order multi-point boundary value problem-s(BVPs). The method is proposed based on the Lagrange interpolation collocation method, but it avoids thenumerical instability of Lagrange interpolation. Numerical results obtained by present method compare with othermethods show that the present method is simple and accurate for higher-order multi-point BVPs, and it is eectivefor solving six order or higher order multi-point BVPs.

A multipoint Birkhoff type boundary value problem

2015 ◽  
Vol 23 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Francesco A. Costabile ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solution ◽  
Collocation Method ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solution ◽  
Multipoint Boundary ◽  
Type Boundary ◽  
Theoretical Results ◽  
Multipoint Boundary Value Problem

AbstractA multipoint boundary value problem is considered. The existence and uniqueness of solution is proved. Then, for the numerical solution, a general collocation method is proposed.Numerical experiments confirm theoretical results.

B*-algebra eigenfunction expansions

1980 ◽  
Vol 86 (3-4) ◽  
pp. 307-314
Author(s):  
Manuel Lopez
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Regular Boundary ◽  
Eigenfunction Expansions ◽  
Expansion Theorem ◽  
Sturm Liouville

SynopsisIn this paper the Sturm-Liouville regular boundary value problem and expansion theorem is extended to functions with values in some B*-algebras.

Qualitative analysis of magnetohydrodynamics stagnation point flow with a novel numerical approach through Shifted Chebyshev collocation method

2021 ◽  
pp. 095440622110568
Author(s):  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Boundary Value Problem ◽  
Stagnation Point ◽  
Collocation Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Partial Slip ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation ◽  
Nonlinear Boundary Value

This paper investigates the third-order nonlinear boundary value problem, resulting from the exact reduction of the Navier-Stokes equation caused by the magnetohydrodynamics boundary layer flow near a stagnation point on a rough plate. The governing partial differential equations are transformed into a nonlinear ordinary differential equation and partial slip boundary conditions by an appropriate similarity transformation. In this previous work, the boundary value problem (BVP) was investigated numerically, and a lot of speculations regarding the existence and behavior of the solutions were carried out. The primary objective of this article is to verify these speculations mathematically. In this work, we have proved that there is a unique solution for all parameters values, and further, the solution has monotonic increasing first derivative. Moreover, the resulting nonlinear boundary value problem is solved by shifted Chebyshev collocation method. We compare the present numerical results with the previous results for the particular physical parameters, concluding that the results are highly accurate. The velocity profiles and streamlines are also plotted to address the significance of the parameters. Our manuscript is a judicial mix between mathematical and numerical methods.

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