A NEW METHOD FOR BOUNDARY VALUE PROBLEMS AND ITS NUMERICAL IMPLEMENTATION

2008 ◽  
Author(s):  
EUAN A. SPENCE
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
New Method ◽  
Numerical Implementation

A new method for calculating eigenvalues with applications to gravity-capillary waves with edge constraints

1983 ◽  
Vol 94 (3) ◽  
pp. 553-564 ◽  
Author(s):  
James Graham-Eagle
Keyword(s):  
Boundary Value Problems ◽  
Variational Formulation ◽  
Boundary Value ◽  
Capillary Waves ◽  
Original Study ◽  
New Method ◽  
Linear Boundary ◽  
Hydrodynamic Problem ◽  
Alternative Means ◽  
Standard Linear

The method to be described provides an alternative means of dealing with certain non-standard linear boundary-value problems. It is developed in several applications to the theory of gravity-capillary waves. The analysis is based on a variational formulation of the hydrodynamic problem, being motivated by and extending the original study by Benjamin and Scott [3].

Numerical Solution of the Beam Equation With Nonuniform Foundation Coefficient

1979 ◽  
Vol 46 (4) ◽  
pp. 901-904 ◽  
Author(s):  
M. Lentini
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
New Method ◽  
Beam Equation ◽  
Infinite Intervals

A new method for computing the solutions of the beam equation is given for the case of the problem of a pile. The method could be used for other problems where it is necessary to solve boundary-value problems for ordinary differential equations over semi-infinite intervals.

scholarly journals Solving Wiener–Hopf problems without kernel factorization

2014 ◽  
Vol 470 (2170) ◽  
pp. 20140304 ◽  
Author(s):  
Darren G. Crowdy ◽  
Elena Luca
Keyword(s):  
Fluid Mechanics ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Kernel Functions ◽  
New Method ◽  
Transform Method ◽  
New Approach ◽  
Mathematical Ideas ◽  
Analytical Functions ◽  
Unified Transform Method

A new approach to solving problems of Wiener–Hopf type is expounded by showing its implementation in two concrete and typical examples from fluid mechanics. The new method adapts mathematical ideas underlying the so-called unified transform method due to A. S. Fokas and collaborators in recent years. The method has the key advantage of avoiding what is usually the most challenging part of the usual Wiener–Hopf approach: the factorization of kernel functions into sectionally analytical functions. Two example boundary value problems, involving both harmonic and biharmonic fields, are solved in detail. The approach leads to fast and accurate schemes for evaluation of the solutions.

scholarly journals Two-dimensional boundary-value problems of elasticity

1946 ◽  
Vol 187 (1008) ◽  
pp. 87-101 ◽  
Keyword(s):  
Boundary Value Problems ◽  
Stress Function ◽  
Boundary Value ◽  
Infinite Plate ◽  
Thin Disk ◽  
New Method ◽  
Two Dimensional ◽  
Airy’S Stress Function ◽  
Dimensional Boundary

A new method of solving two-dimensional problems of elasticity is developed in this paper. Airy’s stress function is not used; but the stress equations of equilibrium are so transformed with the help of consistency equations as to yield simple solutions when the values of the stresses on the boundary are given. The boundaries discussed in this paper are the straight edges of a semi-infinite plate and the circular boundaries of a thin disk. Action of forces and couples in the interior of the plates is chiefly considered.

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