حل عددي برخي معادلات با مشتقات پاره اي با شرايط مرزي غير موضعي مبتني بر فضاي هسته باز توليد

چكيده انگليسي :

Numerical Solution of Some PDEs with Nonlocal Boundary Conditions on the Basis of Reproducing Kernel Space Fereshteh Toutian Isfahani f toutianesfahani@math iut ac ir September 14 2011 Master of Science Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor DR Reza Mokhtari mokhtari@cc iut ac irAdvisor DR Mohammad Reza Raoofi raoo @cc iut ac ir2000 MSC 65M99 35C10Key words Reproducing kernel space nonlocal boundary conditions pseudoparabolic equation nonlinear hyperbolic telegraph equation parabolic inverse problemAbstractNowadays linear nonlinear problems involving partial di erential equations have been became ahot and attractive topics and have been extensively studied both theoretically and experimen tally Some kinds of boundary conditions coupled with partial di erential equations cause somedi culties in solving such problems One of the most applied boundary conditions is the nonlocalboundary condition which comes up when values of the unknown function on the boundary areconnected to the values inside the domain In this thesis after dealing with an approximate methodbased on the reproducing kernel Hilbert space for solving some partial di erential equations suchas a pseduparabolic equation and a nonlinear hyperbolic telegraph equation which endowed with anonlocal boundary condition and an over speci ed condition we present a similar method to solvean inverse problem for parabolic equation with a nonlocal boundary condition and an over speci edcondition The pseduparabolic equation models a variety of important physical processes such aslong dispersive waves the discrepancy between the conductive and thermodynamic temperaturesand aggregation of populations The hyperbolic equation with an integral condition models a va riety of important physical processes such as dynamics of groundwater and population dynamics The inverse problem for parabolic equation with integral over speci ed condition arises from manyimportant applications in heat transfer termoelasticity control theory population dynamics nu clear reactor dynamics medical sciences biochemistry etc Reproducing kernel Hilbert space is avery useful and powerful tool of functional analysis with applications in many diverse paradigmssuch as solving nonlinear partial di erential equations The theory of reproducing kernels wasused for the rst time at the beginning of the 20th century by S Zaremba in his work on boundaryvalue problems for harmonic and biharmonic functions This theory has been successfully ap plied for solving ordinary di erential equations partial di erential equations integral equations integro di erential equations and so on In this thesis rstly we focus on the de nitions andproperties of reproducing kernel spaces associated with a brief history of these spaces Then thesolutions of some partial di erential equations such as the pseduparabolic equation the nonlinearhyperbolic telegraph equation and an inverse coe cient problem for a parabolic equation withnonlocal boundary conditions are given in the form of a convergent series with easily computablecomponents in the reproducing kernel space The advantages of the approach must lie in thefollowing facts The approximate solution converges uniformly to the analytical solution Themethod is mesh free easily implemented and capable in treating various boundary conditions Since the method needs no time discretization there is no matter in which time the approximatesolution is computed from the both elapsed time and stability problem points of view Also wecan evaluate the approximate solution un x t for xed n once and use it over and over

طوطيان اصفهاني، فرشته

حل عددي برخي معادلات با مشتقات پاره اي با شرايط مرزي غير موضعي مبتني بر فضاي هسته باز توليد

معادلات شبه- سهموي , معادلات تلگراف غير خطي هذلولوي , مسئله معكوس براي معادله سهموي