## 35 Reputation

0 years, 348 days

## ODE plot animations...

with the suggestion, I have modified the worksheet but in the plot, i m not obseved any animation only infinity whalve is changing

please check and suggest how to correct it.

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 > with(plots):   cols := [red, blue, green,black]:
 > F:= [Theta](eta): Frame:= Inf-> plots:-display(seq       ( odeplot         ( Ans[k],[eta,Theta(eta)],           eta=0..10,           color=cols[k]         ),         k=1..numelems(KrVals)       )):      plots:-animate(Frame, [Inf], Inf= 0.01..10, frames= 50, size= [900,600],'axes'= 'boxed',labels=[eta,'Theta(eta)']);

## differnet values of Kr in single plot...

Thank you for Quick reply  sir.

How to impliment for differnet values of Kr in single plot with animation.

i have mentioned the graphs which are not in animation mood i want same graph with animation form.

for different values of parameter i need to check the differences in the plots how it will vary.

## substitution of terms in the expression...

How to substitute the expressions as another variables

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 (1)
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 (2)

## Modified equation...

Now the exations are executing for exact solution.

How to simply the equation in some other symbols like m1 m2 m3

To reduce the length of the equation.

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## Remaining terms of the equation...

If i am calculating seperatly for phi0 and phi1 i am getting the similar result as shown in pdf  and the link Here but if i m coupled with second equation temperature equation Theta0 and Theta1 not exicuting showing null sir. How to get this one

I want all terms exact equation. Phi0(y) and Phi1(y) i am getting similarly i need the remaing Theta0(y) and Theta1(y), U0(y), and U1(y)

In the second equation i wrongly mentioned it should be B*G1*Theta1(y) instard of B*G1*Theta0(y)

## details...

Here i m attaching the solution mentioned in the given article exact_solution.pdf

bounday can be any value just for reference consider as 10

## Try...

@KIRAN SAJJAN

Define all the termes before the solution then check once for numerical values it will satisfiy for expression check with it.

@jganding

Thank you

## @jganding I need only the solution for ...

@jganding

I need only the solution for equation 1 sir

Initial conditions can consider as Q(0)=Q0, E(0)=E0, and S(0)=S0

## similar question...

dear sir i have noticed that same question asked by the person @suryakanth which I heve  previously posted up to now i have not seen any update in my post for that i have replied by the same quesstion.

## stream plots...

plot of u1(eta,t)

fieldplot((u1(eta, t)), eta = 0 .. 1, t = 0 .. 1.2)

fieldplot(diff((u1(eta, t)),eta), eta = 0 .. 1, t = 0 .. 1.2)

inf := 3;
M := 2.23606797749; Gr := 5; beta := 1; alpha0 := .1; gama := 3; Ra := 2; Pr := 7.1; R := 2; sigma1 := .2;
in that i taken two different cases when in conditions1) u1(0,t)=1,

case-2) u1(0,t)=t

for diffferent cases i need check the flow pattern with the vecotor plot  above mentioned demo graph

## vector plot for time dependent pde...

some plots i have mentioned but some i m not able to evaluate

urgent required for me. how to plot this type of graph

How to draw this vector plot suggest any previously done file I will do according to that

vector_field_plot.mw

i have posted a few days back only i wont received any answer for this question

## exact and numerical method answer...

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in this i need exact equation of Theta (X,tau)

after substitution of parameter values i need to check the answers for both method

## exact solution...

Dear sir can we find exact solution of the Given pde with IC and BC

restart;
OdeSys := z4*(diff(Theta(X, tau), X, X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Cond := {Theta(0, tau) = 1, Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0};
ans := simplify(eval([OdeSys, Cond], Theta(X, tau) = Theta_exact));
in the given equation i want the value of Theta(X, tau)

By numerical method i can get the solution by substituting the values of parameters but i need to check with exact solution method also

is this possible to solve ?

thank you

## single plot...

@Carl Love according to your suggestions i tried but i m getting only one curve