# Question:first and second order derivative plot of pdes

## Question:first and second order derivative plot of pdes

Maple 2018

How to plot the second order derivative and first oder derivatives plot in time dependent pde and vector plot of  theta(y,t), u(y,t) at y=0..10 and t=0..1

nowhere i found a vector plot of time-dependent pde

how to plot give me suggestions.

in vector plots, flow patterns should show with arrow marks

 > restart;   inf:=10:   pdes:= diff(u(y,t),t)-xi*diff(u(y,t),y)=diff(u(y,t),y\$2)/(1+lambda__t)+Gr*theta(y,t)+Gc*C(y,t)-M*u(y,t)-K*u(y,t),          diff(theta(y,t),t)-xi*diff(theta(y,t),y)=1/Pr*diff(theta(y,t),y\$2)+phi*theta(y,t),          diff(C(y,t),t)-xi*diff(C(y,t),y)=1/Sc*diff(C(y,t),y\$2)-delta*C(y,t)+nu*theta(y,t):   conds:= u(y,0)=0, theta(y,0)=0, C(y,0)=0,           u(0,t)=0, D[1](theta)(0,t)=-1, D[1](C)(0,t)=-1,           u(inf,t)=0, theta(inf,t)=0, C(inf,t)=0:   pars:= { Gr=1, Gc=1, M=1, nu=1, lambda__t=0.5,            Sc=0.78, delta=0.1, phi=0.5, K=0.5, xi=0.5          }
 (1)
 > PrVals:=[0.71, 1.00, 3.00, 7.00]:   colors:=[red, green, blue, black]:   for j from 1 to numelems(PrVals) do       pars1:=`union`( pars, {Pr=PrVals[j]}):       pdSol:= pdsolve( eval([pdes], pars1),                        eval([conds], pars1),                        numeric                      );       plt[j]:=pdSol:-plot( diff(u(y,t),y), y=0, t=0..2, numpoints=200, color=colors[j]);   od:   plots:-display( [seq(plt[j], j=1..numelems(PrVals))]);
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