Second-order boundary value problems with nonhomogeneous boundary conditions (I)

2005 ◽  
Vol 278 (1-2) ◽  
pp. 173-193 ◽  
Author(s):  
Lingju Kong ◽  
Qingkai Kong
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Nonhomogeneous Boundary ◽  
Nonhomogeneous Boundary Conditions

scholarly journals Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the Integrated Forms of High Odd-Order Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Waleed M. Abd-Elhameed ◽  
Eid H. Doha ◽  
Mahmoud A. Bassuony
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Numerical Algorithms ◽  
Condition Numbers ◽  
Test Functions ◽  
Nonhomogeneous Boundary ◽  
Odd Order ◽  
Nonhomogeneous Boundary Conditions ◽  
The Cost

Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made.

Linear second order elliptic equations with Venttsel boundary conditions

1991 ◽  
Vol 118 (3-4) ◽  
pp. 193-207 ◽  
Author(s):  
Yousong Luo ◽  
Neil S. Trudinger
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Existence Result ◽  
Boundary Value ◽  
Second Order ◽  
Classical Solutions ◽  
Schauder Estimate ◽  
Second Order Elliptic Equations

SynopsisWe prove a Schauder estimate for solutions of linear second order elliptic equations with linear Venttsel boundary conditions, and establish an existence result for classical solutions for such boundary value problems.

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