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Question: Numerical solution to an ODE

Question:Numerical solution to an ODE

Stephen Moynihan 48 Maple
ode dsolve numeric differential-equations
March 01 2007
0
Hi, I am trying to solve a 2nd order ODE with linear symmetries (according to odeadvisor!) subject to two boundary conditions. The ODE itself is not particularly pretty (It can't be solved analytically), and it involves quite a lot of other functions that I have to define before hand - sorry if this looks ugly: N:=2: Xi:=1: mu:=0: m:=4: l:=2: sigma:=1: Tau:=0.7: M:=1/(2*(1-(Eta)^2)): a:=Eta: Eta:=Tau*sqrt(2/3): omega:=0.9*m*Eta: g:=r->sqrt((1-2*M/r^(2*N)+2*M*a^2/r^(2*N+2))^(-1)): h:=r->sqrt(r^2*(1+2*M*a^2/r^(2*N+2))): Omega:=r->2*M*a/(r^(2*N+2)+2*M*a^2): f:=r->r/(g(r)*h(r)): V0:=r->f(r)^2*sqrt(h(r))/(r^(N+1))*diff(((f(r)^2)*h(r)/r)*diff(sqrt(h(r))*r^N,r),r): V:=r->V0(r)+f(r)^2*mu^2-(omega-m*Eta)^2+(f(r)^2/(r^2))*(l(l+2*N)-m^2*(1-(r^2/(h(r)^2)))+4*(1-sigma)*(h(r)^2/(r^2)-1)); YY:=diff(V(r),r): XX:=eval(YY,r=1): alpha1:=diff(g(r)^(-2),r): alpha:=r->alpha1/h(r): x:=r->int(g(r)/f(r),r): ODE:= -f(r)*(g(r)^(-1))*diff(f(r)*(g(r)^(-1))*diff(Phi(r),r),r)+2*I*(omega-m*Eta)*f(r)*(g(r)^(-1))*diff(Phi(r),r)+Phi(r)*(V(r)+(omega-m*Eta)^2)=0: Subject to the BC: BC:=Phi_1=1,Phi_p1=(YY*(r-1))/(alpha^2-2*I*alpha*(omega-m*Eta)): I ask Maple to solve the ODE with respect to Phi(r) as follows: dsolve({ODE,BC},numeric,Phi(r)); (Or dsolve({ODE,BC},Phi(r),numeric);) I always get this error message: Error, (in dsolve/numeric/process_input) invalid specification of initial conditions, got D(phi)(1) = 5.840594046*(r-1)/(alpha^2+.1866666666*I*alpha*6^(1/2)) I take it I have defined something incorrectly above - but I can't for the life of me see what. Please help; I have been trying to solve this thing for weeks. Thanks for your help, Steve
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