TY - JOUR
T1 - Solution of boundary and eigenvalue problems for second-order elliptic operators in the plane using pseudoanalytic formal powers
AU - Castillo Pérez, Raúl
AU - Kravchenko, Vladislav V.
AU - Reséndiz Vázquez, Rabindranath
PY - 2011/3/15
Y1 - 2011/3/15
N2 - We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D = diva pa grad + q in the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q with the aid of pseudoanalytic function theory a complete system of null solutions of the operator can be constructed following a simple algorithm consisting in recursive integration. This system of solutions is used for solving boundary value and spectral problems for the operator D in bounded simply connected domains. We study theoretical and numerical aspects of the method.
AB - We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D = diva pa grad + q in the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q with the aid of pseudoanalytic function theory a complete system of null solutions of the operator can be constructed following a simple algorithm consisting in recursive integration. This system of solutions is used for solving boundary value and spectral problems for the operator D in bounded simply connected domains. We study theoretical and numerical aspects of the method.
KW - Schrödinger equation
KW - Vekua equation
KW - boundary value problem
KW - eigenvalue problem
KW - pseudoanalytic function
UR - http://www.scopus.com/inward/record.url?scp=79951747659&partnerID=8YFLogxK
U2 - 10.1002/mma.1372
DO - 10.1002/mma.1372
M3 - Artículo
SN - 0170-4214
VL - 34
SP - 455
EP - 468
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 4
ER -