IJPAM: Volume 54, No. 3 (2009)

NUMERICAL SOLUTION OF TWO-POINT BOUNDARY
VALUE PROBLEMS WITH MIXED BOUNDARY
CONDITIONS USING WEIGHTED RESIDUAL METHOD

S.A. Odejide$^1$, O.A. Adewunmi$^2$
$^{1,2}$Department of Mathematics
Obafemi Awolowo University
Ile-Ife, NIGERIA
$^1$e-mails: [email protected]
$^2$e-mails: [email protected]


Abstract.In this paper, we examined the two-point boundary value problems of the form

\begin{displaymath}L(y) = f(x,y) \end{displaymath}

subject to the mixed boundary conditions
\begin{align*}
& y'(a) - cy(a) = A\,,\\
& y'(b) + dy(b) = B\,,
\end{align*}
where $ L $ is the differential operator (linear or non-liear) involving spartial derivatives of y, $c\geq0$, $d\geq0$, $c+d>0$, A and B are constants and and $x\in[a, b]$. These equations are solved using weighted residual method. An approximating function with some constants is assumed to satisfy the boundary conditions. These constants are determined using various methods such as Galerkin method, collocation method, partion method, moment method and least-squares method. The results obtained from each method were compared with the analytical solutions.

Received: August 7, 2006

AMS Subject Classification: 76M10

Key Words and Phrases: mixed boundary conditions, weighted residual methods, weight functions, residual error

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 3