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Tamour_Zubair

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Need to Solve System of ODE Using RK-4...

Tamour_Zubair 80 Maple 2021
ode homework numeric
September 06 2023
1 11

Hello Everyone;

I need help to solve the following system using rk-4 method

restart;
NULL;
NULL;
C := 1.0;
gK := 36.0;
gNa := 120.0;
gL := 0.3;
VK := -77.0;
VNa := 50.0;
VL := -54.0;
III := 20;
alpha_n := 0.01*(v(t) + 55.0)/(1 - exp(-1.0/10.0*v(t) - 11.0/2.0));
beta_n := 0.125*exp((-v(t))/80.0 + (-1)*13.0/16.0);
alpha_m := 0.1*(v(t) + 40.0)/(1 - exp(-1.0/10.0*v(t) - 4.0));
beta_m := 4.0*exp(-1.0/18.0*v(t) - 65.0/18.0);
alpha_h := 0.07*exp((-1)*(v(t) + 65.0)/20.0);
beta_h := 1/(1.0 + exp((-v(t) + 35.0)/10.0));

dsys1 := {diff(h(t), t) = alpha_h*(1 - h(t)) - beta_h*h(t), diff(m(t), t) = alpha_m*(1 - m(t)) - beta_m*m(t), diff(n(t), t) = alpha_n*(1 - n(t)) - beta_n(t), diff(v(t), t) = III - gK*n(t)^4*(v(t) - VK) - gNa*m(t)^3*h(t)*(v(t) - VNa) - gL*(v(t) - VL), h(0) = 0.9996937394, m(0) = 0.02890553447, n(0) = 0.2445865495, v(0) = -70};

Analytical Solution of Nonlinear ODE ...

Tamour_Zubair 80 Maple 2021
ode nonlinear differential-equations
September 04 2023
1 4

Hello Everyone;

Can anybody help me to solve the analytical solution of the following ODE?
AAS := C*diff(y(t), t) + (-B0*y(t)^3 - B1*y(t)^2 - B2*y(t) - B3);y[0] := 1

C,B0,B1,B2 are constants.

Need to Solve Nonlinear ODE...

Tamour_Zubair 80 Maple 2021
ode dsolve nonlinear
August 28 2023
1 0

Hello Everyone;

I need to solve the following nonlinear ODE

C*diff(y(x), x) + (-B0*y(x)^3 - B1*y(x)^2 - B2*y(x) - B3) = 0, y(0)=B4

where B0,B1,B2,B3 and B4 are constants. I am trying in Maple 2021, but receiving solution in the form of integral. Is that any other ways that I will be able exact solution. Maple sheet is atatched. I am waiting for your kind respose.

Thanks

Question1.mw

> 

restart
 
> 

infolevel[dsolve] := 4

4

 (1)
> 

ode22 := C*(diff(y(x), x))-B0*y(x)^3-B1*y(x)^2-B2*y(x)-B3 = 0

C*(diff(y(x), x))-B0*y(x)^3-B1*y(x)^2-B2*y(x)-B3 = 0

 (2)
> 

solll := dsolve(ode22, implicit, useInt)

Methods for first order ODEs:

  

--- Trying classification methods ---

  

trying a quadrature

  

trying 1st order linear

  

trying Bernoulli

  

trying separable

  

<- separable successful

  

x-Intat(C/(B0*_a^3+B1*_a^2+B2*_a+B3), _a = y(x))+_C1 = 0

 (3)
> 

ode[257] := C*(diff(y(x), x))-B0*y(x)^3-B1*y(x)^2-B2*y(x)-B3 = 0

C*(diff(y(x), x))-B0*y(x)^3-B1*y(x)^2-B2*y(x)-B3 = 0

 (4)
> 

dsolve(ode[257], implicit)

Methods for first order ODEs:

  

--- Trying classification methods ---

  

trying a quadrature

  

trying 1st order linear

  

trying Bernoulli

  

trying separable

  

<- separable successful

  

x-Intat(C/(B0*_a^3+B1*_a^2+B2*_a+B3), _a = y(x))+_C1 = 0

 (5)
> 

NULL

Download Question1.mw

not working dsolve comand for ODEs...

Tamour_Zubair 80 Maple 2022
ode dsolve numeric
May 11 2023
1 0

Hello Everyone;

Hope you are fine. I I have make a code but there is error and dsolve comand is working. I also need to plot. Kindly help me. I am waiting kind response. Code is attached.

> 

restart; Cm := 1.0; ENa := 50.0; EK := -77.0; ELeak := -54.387; gNa := 120.0; gK := 36.0; gLeak := .3; II := piecewise(`and`(t >= 10, t <= 40), 10.0, 0.); alpha_m := proc (V) .1*(V+40.0)/(1.0-exp((-1)*(V+40.0)/10.0)) end proc; beta_m := proc (V) 4.0*exp((-1)*(V+65.0)/18.0) end proc; alpha_h := proc (V) 0.7e-1*exp((-1)*(V+65.0)/20.0) end proc; beta_h := proc (V) 1.0/(1.0+exp((-1)*(V+35.0)/10.0)) end proc; alpha_n := proc (V) 0.1e-1*(V+55.0)/(1.0-exp((-1)*(V+55.0)/10.0)) end proc; beta_n := proc (V) .125*exp((-1)*(V+65.0)/80.0) end proc; eq1 := diff(V(t), t) = (II-gNa*m(t)^3*h(t)*(V(t)-ENa)-gK*n(t)^4*(V(t)-EK)-gLeak*(V(t)-ELeak))/Cm; eq2 := diff(m(t), t) = alpha_m(V(t))*(1-m(t))-beta_m(V(t))*m(t); eq3 := diff(h(t), t) = alpha_h(V(t))*(1-h(t))-beta_h(V(t))*h(t); eq4 := diff(n(t), t) = alpha_n(V(t))*(1-n(t))-beta_n(V(t))*n(t); ics := {V(0) = -65, h(0) = .6, m(0) = 0.5e-1, n(0) = .32}

1.0

  

50.0

  

-77.0

  

-54.387

  

120.0

  

36.0

  

.3

  

20

  

proc (V) .1*(V+40.0)/(1.0-exp((-1)*(V+40.0)/10.0)) end proc

  

proc (V) 4.0*exp((-1)*(V+65.0)/18.0) end proc

  

proc (V) 0.7e-1*exp((-1)*(V+65.0)/20.0) end proc

  

proc (V) 1.0/(1.0+exp((-1)*(V+35.0)/10.0)) end proc

  

proc (V) 0.1e-1*(V+55.0)/(1.0-exp((-1)*(V+55.0)/10.0)) end proc

  

proc (V) .125*exp((-1)*(V+65.0)/80.0) end proc

  

diff(V(t), t) = 3.683900000-120.0000000*m(t)^3*h(t)*(V(t)-50.0)-36.00000000*n(t)^4*(V(t)+77.0)-.3000000000*V(t)

  

diff(m(t), t) = .1*(V(t)+40.0)*(1-m(t))/(1.0-exp(-.1000000000*V(t)-4.000000000))-4.0*exp(-0.5555555556e-1*V(t)-3.611111111)*m(t)

  

diff(h(t), t) = 0.7e-1*exp(-0.5000000000e-1*V(t)-3.250000000)*(1-h(t))-1.0*h(t)/(1.0+exp(-.1000000000*V(t)-3.500000000))

  

diff(n(t), t) = 0.1e-1*(V(t)+55.0)*(1-n(t))/(1.0-exp(-.1000000000*V(t)-5.500000000))-.125*exp(-0.1250000000e-1*V(t)-.8125000000)*n(t)

  

{V(0) = -65, h(0) = .6, m(0) = 0.5e-1, n(0) = .32}

 (1)
> 

sol := dsolve({eq1, eq2, eq3, eq4, ics})

Error, (in dsolve) invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({list, set})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received {{V(0) = -65, h(0) = 3/5, m(0) = 1/20, n(0) = 8/25}}

  
> 

NULL

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Thanks

Make my Own Code and Call to other file ...

Tamour_Zubair 80 Maple 2021
incomplete-question
November 23 2022
0 0

Hello;

Hope you are fine. I need to learn how can I call my code in the other file of maple, define new value for A and can get results. For this purpose, I just take an simple example as

questionmaple.mw

> 

restart; A := 5; B := 10; AAA[0] := 10; for i from 0 while i <= A do AAA[i+1] := B*i*AAA[0] end do

5

  

10

  

10

  

0

  

100

  

200

  

300

  

400

  

500

 (1)
 

``

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