ayo

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5 years, 349 days

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These are questions asked by ayo

Please how can i obtain analytical siolution of the system of pde with maple

pde1 := diff(u(x, t), t) = (1/50)*(diff(u(x, t), x, x))+1-4*u(x, t)+u(x, t)^2*v(x, t);
pde2 := diff(v(x, t), t) = (1/50)*(diff(v(x, t), x, x))+3*u(x, t)-u(x, t)^2*v(x, t);
u(x, 0) = 1+sin(2*Pi*x), v(x, 0) = 3, u(0, t) = u(1, t) and u(1, t) = 1, v(0, t) = v(1, t) and v(1, t) = 3;

 

restart; with(plots);
G := 1; M := .1; R := 1; P := .72; alpha := .1; phi := 1; K := 1; n := 2; beta := 1;
                               1
                              0.1
                               1
                              0.72
                              0.1
                               1
                               1
                               2
                               1
ode1 := {(1+(4/3)*R)*(diff(theta(x), x, x))+(1/2)*P*f(x)*(diff(theta(x), x))+alpha*theta(x) = 0, n*(diff(f(x), x, x))^(n-1)*(diff(f(x), x, x, x))+f(x)*(diff(f(x), x, x))/(n+1)+G*theta(x)-M*(diff(f(x), x)) = 0, f(0) = 0, theta(10) = 0, (D(f))(0) = beta*K*((D@@2)(f))(0), (D(f))(10) = 1, (D(theta))(0) = -phi*(1-theta(0))};
 /7  d  / d          \                     / d          \
{ - --- |--- theta(x)| + 0.3600000000 f(x) |--- theta(x)|
 \3  dx \ dx         /                     \ dx         /

                         / d  / d      \\ / d  / d  / d      \\\
   + 0.1 theta(x) = 0, 2 |--- |--- f(x)|| |--- |--- |--- f(x)|||
                         \ dx \ dx     // \ dx \ dx \ dx     ///

     1      / d  / d      \\                  / d      \      
   + - f(x) |--- |--- f(x)|| + theta(x) - 0.1 |--- f(x)| = 0,
     3      \ dx \ dx     //                  \ dx     /      

  f(0) = 0, theta(10) = 0, D(f)(0) = @@(D, 2)(f)(0),

                                           \
  D(f)(10) = 1, D(theta)(0) = -1 + theta(0) }
                                           /
dsol := dsolve(ode1, numeric, method = bvp[midrich], range = 0 .. 10);
Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

 

How do i implement Runge-Kutta of order 6 for a sytem of boundary value problems on maple

1.How can i solve 1000 simultaneous equations with 1000 unknoowns on maple?

2. how can apply thomas algorithm on maple?

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