Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bou...Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bounded or unbounded domain in R~3 and obtain the error estimates of the approximate solution in energy norm and local maximum norm.展开更多
§1.IntroductionThis paper deals with linear partial differential operators with real principalsymbol.Let P(x,D)be such an operator of mth order with C~∞ coefficients definedin an open subset Ω of R^n and p_m(x,...§1.IntroductionThis paper deals with linear partial differential operators with real principalsymbol.Let P(x,D)be such an operator of mth order with C~∞ coefficients definedin an open subset Ω of R^n and p_m(x,ξ)be its principal symbol.According to thedefinition given by Duistermaat and Hmander(see[1]),P(x,D)is called ofprincipal type at x^0 ∈Ω if for any ξ∈R^n\0 satisfying p_m(x^0,ξ)=0,x=x^0 is not theprojection in Ω of the bicharacteristic strip of P(x,D)through(x^0,ξ).Under thiscondition,they proved that there exists a neighborhood U of x^0,U,such that forany real number s,展开更多
基金China State Major Key Project for Basic Researches
文摘Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bounded or unbounded domain in R~3 and obtain the error estimates of the approximate solution in energy norm and local maximum norm.
文摘§1.IntroductionThis paper deals with linear partial differential operators with real principalsymbol.Let P(x,D)be such an operator of mth order with C~∞ coefficients definedin an open subset Ω of R^n and p_m(x,ξ)be its principal symbol.According to thedefinition given by Duistermaat and Hmander(see[1]),P(x,D)is called ofprincipal type at x^0 ∈Ω if for any ξ∈R^n\0 satisfying p_m(x^0,ξ)=0,x=x^0 is not theprojection in Ω of the bicharacteristic strip of P(x,D)through(x^0,ξ).Under thiscondition,they proved that there exists a neighborhood U of x^0,U,such that forany real number s,
