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Prakash J

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These are questions asked by Prakash J

How do I find a unknown values in bounda...

Prakash J 100 Maple 18
syntax rootfinding
June 06 2023
1 0

I have some ODE system contains unknown variables with  boundary conditions  (see the attachment). How to solve these system and find the vales of unknown variables.

In this problem, the boundary conditions tends to 0, when x tends to infinity.  BVP_with_parameters.mw
 

restart

eq1 := f(x) = x+a[1]*x^2-(1/48)*sqrt(2)*a[1]*x^4-(1/120)*a[1]^2*sqrt(2)*x^5;

h(x) = -0.3535533905e-3*x^5*a[2]*a[1]*a[3]-0.3333333334e-9*x^5*a[3]*a[2]^4+0.4166666668e-7*x^4*a[2]*a[3]^3-0.3333333334e-9*x^5*a[2]^2*a[3]^3-0.5000000000e-9*x^5*a[3]^2*a[2]^3+0.1250000000e-6*x^4*a[3]*a[2]^3-0.8333333336e-10*x^5*a[2]*a[3]^4+0.1250000000e-6*x^4*a[3]^2*a[2]^2-0.8333333336e-10*x^5*a[2]^5+0.4166666668e-7*x^4*a[2]^4+a[3]*x-0.1473139128e-1*x^4*a[1]*a[3]+0.2946278254e-1*x^4*a[1]*a[2]-0.3240906080e-3*x^5*a[1]*a[2]^2+0.2798964342e-5*x^5*a[2]*a[3]^2+0.4714045206e-5*x^5*a[3]*a[2]^2-0.6629126071e-3*x^4*a[3]*a[2]+0.7812499998e-3*x^5*a[3]-0.2946278254e-1*x^3*a[3]-0.5892556508e-3*x^4*a[2]^2+0.1915080866e-5*x^5*a[2]^3+0.5892556509e-1*x^3*a[2]-0.4687500000e-2*x^5*a[2]+0.5000000000e-2*a[2]^2*x^2-0.1666666667e-4*x^3*a[2]^3+0.5000000000e-2*a[2]*x^2*a[3]-0.3333333334e-4*x^3*a[3]*a[2]^2-0.1666666667e-4*x^3*a[2]*a[3]^2+1.

 (1)

bcs := f(0) = 0, (D(f))(0) = 1, f(10) = 0, g(0) = 1, g(10) = 0, h(0) = 1, h(10) = 0;

f(0) = 0, (D(f))(0) = 1, f(10) = 0, g(0) = 1, g(10) = 0, h(0) = 1, h(10) = 0

 (2)

sol := dsolve([{f(x), g(x), h(x)}, bcs], numeric)

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

  

``

 

How to solve this PDE system ?...

Prakash J 100 Maple 2018
homework pde differential-equations
May 18 2023
1 2

eq1:=( d)/(dt)u+(d^(2))/(dy^(2))u + s*( d)/(dy)u + delta * theta = 0;

eq2:=( d)/(dt)theta + (d^(2))/(dy^(2))theta + s*Pr*( d)/(dy)theta +lambda* exp(theta/(1 +(epsilon*theta))) = 0; 

initial and boundary conditons   

t <=0; u = theta = 0, for 0 <= y  <= 1   

t> 0;  u =0, theta = 0   at  y = 0;  

t> 0;  u =1, theta = 0   at   y = 1  ;

where, s, epsilon, Pr, lambda, delta are arbitrary parameters

How to solve differential equations with...

Prakash J 100 Maple 18
ode homework dsolve
April 26 2023
2 6

eq1 := diff(f(x), x, x, x)+(1/2)*cos(alpha)*x*(diff(f(x), x, x))+(1/2)*sin(alpha)*f(x)*(diff(f(x), x, x)) = 0;

eq2 := diff(g(x), x, x)+diff(g(x), x)+(diff(g(x), x))*(diff(h(x), x))+cos(alpha)*x*(diff(g(x), x))+sin(alpha)*f(x)*g(x) = 0;

eq3 := diff(g(x), x, x)+diff(h(x), x, x)+1/2*(cos(alpha)*x+sin(alpha)*f(x)) = 0

ics := f(0) = 0, (D(f))(0) = 1, ((D@@2)(f))(0) = a[1], g(0) = 1, (D(g))(0) = a[2], h(0) = 1, (D(h))(0) = a[3];

How to plot this equation?...

Prakash J 100 Maple 2018
integration piecewise plotting
June 15 2022
1 0

 

where p, q, r, a are positive constants and phi(0) be a initial condition

How to solve ode system with equilibrium...

Prakash J 100 Maple 2018
April 21 2022
1 1

eq1 := diff(x(t), t) = x(K[1]-x(t))-p*x(t-tau[1])*y(t); eq2 := diff(y(t), t) = y(K[2]-x(t))-q*y(t-tau[2])*x(t);
(x*, y*):= (p*K[2]-k[1])/(p*q-1), (q*K[1]-k[2])/(p*q-1);

where, k_1, k_2, p, q, tau_1, tau_2 are positive constants

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