TY - JOUR
T1 - A new transform method II: the global relation and boundary-value problems in polar coordinates
AU - Spence, Euan A
AU - Fokas, A S
PY - 2010
Y1 - 2010
N2 - A new method for solving boundary-value problems (BVPs) for linear and certain nonlinear PDEs was introduced by one of the authors in the late 1990s. For linear PDEs, this method constructs novel integral representations (IRs) that are formulated in the Fourier (transform) space. In a previous paper, a simplified way of obtaining these representations was presented. In the current paper, first, the second ingredient of the new method, namely the derivation of the so-called ‘global relation’ (GR)—an equation involving transforms of the boundary values—is presented. Then, using the GR as well as the IR derived in the previous paper, certain BVPs in polar coordinates are solved. These BVPs elucidate the fact that this method has substantial advantages over the classical transform method.
AB - A new method for solving boundary-value problems (BVPs) for linear and certain nonlinear PDEs was introduced by one of the authors in the late 1990s. For linear PDEs, this method constructs novel integral representations (IRs) that are formulated in the Fourier (transform) space. In a previous paper, a simplified way of obtaining these representations was presented. In the current paper, first, the second ingredient of the new method, namely the derivation of the so-called ‘global relation’ (GR)—an equation involving transforms of the boundary values—is presented. Then, using the GR as well as the IR derived in the previous paper, certain BVPs in polar coordinates are solved. These BVPs elucidate the fact that this method has substantial advantages over the classical transform method.
UR - http://www.scopus.com/inward/record.url?scp=77955974995&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1098/rspa.2009.0513
U2 - 10.1098/rspa.2009.0513
DO - 10.1098/rspa.2009.0513
M3 - Article
SN - 1364-5021
VL - 466
SP - 2283
EP - 2307
JO - Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
JF - Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
IS - 2120
ER -