Items tagged with nonlinear

I meet a interesting nonlinear system in the analysis of an mechanics problem. This system can be shown as following:

wherein, the X and Y is the solutions. A, B, S, and T is the symbolic parameters.

I want to express X and Y with A, B, S, T. Who can give me a help, thanks a lot!

PS:the mw file is given here.

A_symbolic_nonlinear_system.mw

Im trying to solve 12 equations with 12 variables but I can't solve. Please help and advise me to solve this problem. Iproject3.mw
project3.mw

 

 

 

Dears;

Hope everyone is fine. I am try to find the numerical solutions of system of nonlinear algabric equation via newton's raphson method in the attached file but failed. Please see the attachment and try to correct. You can solve it least square method if possible. I am waiting your positive response. 

Help_in_Newton.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Email: muhammadusman@pku.edu.cn

hy

i have to develop a code i which i have system of nonlinear equation 

i have to generate the matrix of that nonlinear equation then i want to do or apply any method say newton method and make a loop which help us to find a solution using some tolerance 

at the end i get a result in form of a table which give nth matrix then value of function matrix at nth value then error i-e xn-x(n-1) 

thanx in advance

hi..i have a problem for solving this nonlinear differential equationerror.mw

restart; Digite := 200; L := 100*10^(-9)

1/10000000

(1)

EQ11 := -3.000000000*10^(-8)+3.815358072*sin(3.141592654*10^7*x)+9.534375000*10^(-30)*(diff(w(x), x, x, x, x))-2.383593750*10^(-60)*(diff(w(x), x, x, x, x, x, x))-5.085000000*10^(-13)*(diff(w(x), x))*(diff(u(x), x, x))-7.627500000*10^(-13)*(diff(w(x), x))^2*(diff(w(x), x, x))-5.085000000*10^(-13)*(diff(w(x), x, x))*(diff(u(x), x))+0.2410290000e-5*(diff(w(x), x, x)):

EQ2 := 5.650000000*10^(-20)*(diff(u(x), x, x, x, x))-226000000000*(diff(u(x), x, x))-226000000000*(diff(w(x), x))*(diff(w(x), x, x)):

dsys3 := {EQ11, EQ2, u(0) = 0, u(L) = 0, w(0) = 0, w(L) = 0, (D(u))(0) = 0, (D(u))(L) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(L) = 0, ((D@@4)(w))(0) = 0, ((D@@4)(w))(L) = 0}; res := dsolve(dsys3, numeric, initmesh = 1024, abserr = 0.1e-4); res(0.1e-9)

res(0.1e-9)

(2)

############################################################CHANGE OF VARIABLE:::           x=y*L

bcs := {u(0) = 0, u(L) = 0, w(0) = 0, w(L) = 0, (D(u))(0) = 0, (D(u))(L) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(L) = 0, ((D@@4)(w))(0) = 0, ((D@@4)(w))(L) = 0}; sys := {EQ11, EQ2}; sys2 := PDEtools:-dchange({x = L*y, u(x) = g2(y), w(x) = g1(y)}, sys, [g1, g2, y]); solve(sys2, {diff(g2(y), y, y, y, y), diff(g1(y), y, y, y, y, y, y)}); bcs3 := {g1(0) = 0, g1(1) = 0, g2(0) = 0, g2(1) = 0, (D(g2))(0) = 0, (D(g2))(1) = 0, ((D@@2)(g1))(0) = 0, ((D@@2)(g1))(1) = 0, ((D@@4)(g1))(0) = 0, ((D@@4)(g1))(1) = 0}; res3 := dsolve(`union`(sys2, bcs3), numeric, maxmesh = 2024, abserr = 0.1e-4); plots:-odeplot(res3, [seq([y, (cat(g, i))(y)], i = 1 .. 2)], 0 .. 1)

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

``

 

Download error.mw

please help me

thanks...

 

Dear all,

I would like to solve the following non linear ODE with Maple, but I am no able. I do not know if it is possible, beccause it is nolinear.

I really appreciate any advice or help. This is the equation:

y'(x) - (Q - x*p0*(exp(alpha-beta*y(x)))/(1+exp(alpha-beta*y(x))))^2=0

thanks a lot

Hy Prof.

Please help me or guide me to get idea to solve Nonlinear coupled PDEwith MAPLE.Dr.Sam Dao could please help me as I saw your YOUTUBE lecturer which very helpful to me and please give some idea about my topic.

pde[1] := diff(u(x, t), t)-D(diff(u(x, t), x, x)) = alpha*u(x, t)*(1-v(x, t))

pde[2] := diff(v(x, t), t)-E(diff(v(x, t), x, x)) = beta*v(x, t)*(1-u(x, t))

Thanks in advance and answer is highly appricaited 

hi...please help me for solve this nonlinear equations with pdsolve

thanksoffcenter2.mw

La := .25; Lb := 0.1e-1

h := 0.4e-2

rho := 7900

E := 0.200e12

nu := .3

ve := 5

g := 9.8

M := .5

Z0 := 0.1e-2

K := 5/6

C := sqrt(E/rho)

NULL

 

PDE[1] := diff(u(x, t), x, x)+(diff(w(x, t), x))*(diff(w(x, t), x, x)) = (diff(u(x, t), t, t))/C^2

diff(diff(u(x, t), x), x)+(diff(w(x, t), x))*(diff(diff(w(x, t), x), x)) = 0.3949999999e-7*(diff(diff(u(x, t), t), t))

(1)

PDE[2] := K*(diff(phi(x, t), x)+diff(w(x, t), x, x))/(2*(1+nu))+(diff(w(x, t), x))*(diff(u(x, t), x, x))+(diff(u(x, t), x))*(diff(w(x, t), x, x))+(3/2)*(diff(w(x, t), x, x))*(diff(w(x, t), x))^2 = (diff(w(x, t), t, t))/C^2

.3205128205*(diff(phi(x, t), x))+.3205128205*(diff(diff(w(x, t), x), x))+(diff(w(x, t), x))*(diff(diff(u(x, t), x), x))+(diff(u(x, t), x))*(diff(diff(w(x, t), x), x))+(3/2)*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^2 = 0.3949999999e-7*(diff(diff(w(x, t), t), t))

(2)

 

PDE[3] := diff(phi(x, t), x, x)-6*K*(diff(w(x, t), x)+phi(x, t))/(h^2*(1+nu)) = (diff(phi(x, t), t, t))/C^2

diff(diff(phi(x, t), x), x)-240384.6154*(diff(w(x, t), x))-240384.6154*phi(x, t) = 0.3949999999e-7*(diff(diff(phi(x, t), t), t))

(3)

 

 

#####################################

(4)

at x= La

PDE[a1] := diff(u(x, t), x)+(1/2)*(diff(w(x, t), x))^2-M*(g-(diff(u(x, t), t, t))-Z0*(diff(phi(x, t), t, t)))/(E*Lb*h) = 0

diff(u(x, t), x)+(1/2)*(diff(w(x, t), x))^2-0.6125000000e-6+0.6250000000e-7*(diff(diff(u(x, t), t), t))+0.6250000000e-10*(diff(diff(phi(x, t), t), t)) = 0

(5)

PDE[a2] := diff(phi(x, t), x)-12*M*Z0*(g-(diff(u(x, t), t, t))-Z0*(diff(phi(x, t), t, t)))/(E*Lb*h^3) = 0

diff(phi(x, t), x)-0.4593750000e-3+0.4687500000e-4*(diff(diff(u(x, t), t), t))+0.4687500000e-7*(diff(diff(phi(x, t), t), t)) = 0

(6)

PDE[a3] := w(x, t) = 0

w(x, t) = 0

(7)

NULL

############################################

``

at x=0 NULL

(8)

PDE[b1] := u(x, t) = 0 

PDE[b2] := w(x, t) = 0

PDE[b3] := diff(phi(x, t), x) = 0

diff(phi(x, t), x) = 0

(9)

################################################

at t=0 for x= [0,La]

u(x, t) = 0

u(x, t) = 0

(10)

w(x, t) = 0

w(x, t) = 0

(11)

phi(x, t) = 0

phi(x, t) = 0

(12)

diff(phi(x, t), t) = 0

diff(phi(x, t), t) = 0

(13)

diff(w(x, t), t) = 0

diff(w(x, t), t) = 0

(14)

diff(phi(x, t), t, t) = 0

diff(diff(phi(x, t), t), t) = 0

(15)

diff(w(x, t), t, t) = 0

diff(diff(w(x, t), t), t) = 0

(16)

######################################################

at t=0 for x= [0,La)

diff(u(x, t), t) = 0

diff(u(x, t), t) = 0

(17)

diff(u(x, t), t, t) = 0

diff(diff(u(x, t), t), t) = 0

(18)

###################################################

at t=0 for x=La

NULL

diff(u(x, t), t) = -ve

diff(u(x, t), t) = -5

(19)

diff(u(x, t), t, t) = g

diff(diff(u(x, t), t), t) = 9.8

(20)

NULL

NULL

 

Download offcenter2.mw

Hi everyone!

I have a problem solving the nonlinear ode (as attached below). I got this error ---> Error, (in fproc) unable to store '-1.32352941215398+(-0.441176470717993e-1, -0.)' when datatype=float[8]

1) Could someone please explain to me what does the unable store .... error means? 

and i will be grateful if you could help me finding the solution out. Thanks in advance



Dear All,

I have a problem solving the attached nonlinear system of equations using shooting method.
I will be grateful if you could help me finding the solutions out.

 

restart; Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot);
with(plots);
N1 := 1.0; N2 := 2.0; N3 := .5; Bt := 6; Re_m := N1*Bt; gamma1 := 1;
FNS := {f(eta), fp(eta), fpp(eta), g(eta), gp(eta), m(eta), mp(eta), n(eta), np(eta), fppp(eta)};
ODE := {diff(f(eta), eta) = fp(eta), diff(fp(eta), eta) = fpp(eta), diff(fpp(eta), eta) = fppp(eta), diff(g(eta), eta) = gp(eta), diff(gp(eta), eta) = N1*(2.*g(eta)+(eta-2.*f(eta)).gp(eta)+2.*g(eta)*fp(eta)+2.*N2.N3.(m(eta).np(eta)-n(eta).mp(eta))), diff(m(eta), eta) = mp(eta), diff(mp(eta), eta) = Re_m.(m(eta)+(eta-2.*f(eta)).mp(eta)+2.*m(eta)*fp(eta)), diff(n(eta), eta) = np(eta), diff(np(eta), eta) = Re_m.(2.*n(eta)+(eta-2.*f(eta)).np(eta)+2.*N2/N3.m(eta).gp(eta)), diff(fppp(eta), eta) = N1*(3.*fpp(eta)+(eta-2.*f(eta)).fppp(eta)-2.*N2.N2.m(eta).(diff(mp(eta), eta)))};
blt := 1.0; IC := {f(0) = 0, fp(0) = 0, fpp(0) = alpha1, g(0) = 1, gp(0) = beta1, m(0) = 0, mp(0) = beta2, n(0) = 0, np(0) = beta3, fppp(0) = alpha2};
BC := {f(blt) = .5, fp(blt) = 0, g(blt) = 0, m(blt) = 1, n(blt) = 1};
infolevel[shoot] := 1;
S := shoot(ODE, IC, BC, FNS, [alpha1 = 1.425, alpha2 = .425, beta1 = -1.31, beta2 = 1.00, beta3 = 1.29]);
Error, (in isolate) cannot isolate for a function when it appears with different arguments
p := odeplot(S, [eta, fp(eta)], 0 .. 15);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
display(p);
Error, (in plots:-display) expecting plot structure but received: p
p2 := odeplot(S, [eta, theta(eta)], 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
display(p2);
Error, (in plots:-display) expecting plot structure but received: p2

 

 

Dear Community,

I've made a nonlinear curve fit with the Minimize routine (see attachment). What would be an easy and elegant way to rerun the model (Model) with the fitted values of a, b, c and plot the result together with the measured points in the same chart? I'm stuck here.

Tx in advance,

best regards

Andras

BroSzem_Data.xlsx

Nonlin_Curve_Fit.mw

 

      General description of the method of solving underdetermined systems of equations. As a particular application of the idea proposed a universal method  kinematic analysis for all kinds of linkage (lever) mechanisms. With the description and examples.
      The method can be used for powerful CAD linkages.

Description: Calculation_method_of_linkages.pdf

Attachment:
figure_1.mw
figure_2.mw

Or all in one
Calculation_method_of_linkages_(with_attach.).pdf


        Some examples of a much larger number calculated by the proposed method. Examples gathered here not to look for them on the forum and opportunity to demonstrate the method.  Among the examples, I think, there are very complicated.

https://vk.com/doc242471809_408704758
https://vk.com/doc242471809_408704572
https://vk.com/doc242471809_376439263
https://vk.com/doc242471809_402619761
https://vk.com/doc242471809_402610228
https://vk.com/doc242471809_401188803
https://vk.com/doc242471809_400465891
https://vk.com/doc242471809_400711315
https://vk.com/doc242471809_387358164
https://vk.com/doc242471809_380837279
https://vk.com/doc242471809_379935473
https://vk.com/doc242471809_380217387
https://vk.com/doc242471809_363266817
https://vk.com/doc242471809_353980472
https://vk.com/doc242471809_375452868
https://vk.com/doc242471809_353988163 
https://vk.com/doc242471809_353986884 
https://vk.com/doc242471809_353987119
https://vk.com/doc242471809_324249241
https://vk.com/doc242471809_324102889
https://vk.com/doc242471809_322219275
https://vk.com/doc242471809_437298137
https://vk.com/doc242471809_437308238
https://vk.com/doc242471809_437308241
https://vk.com/doc242471809_437308243
https://vk.com/doc242471809_437308245
https://vk.com/doc242471809_437308246
https://vk.com/doc242471809_437401651
https://vk.com/doc242471809_437664558

 

 

hello every one.please help me with solving this equations.i can not solve this and i need it.thanks


eq1 := (cos(beta2)-1)*w11-sin(beta2)*w12+(cos(alpha2)-1)*z11-sin(alpha2)*z12-cos(delta2) = 0; eq2 := (cos(beta2)-1)*w12+sin(beta2)*w11+(cos(alpha2)-1)*z12+sin(alpha2)*z11-2*sin(delta2) = 0; eq3 := (cos(beta3)-1)*w11-sin(beta3)*w12+(cos(alpha3)-1)*z11-sin(alpha3)*z12-3*cos(delta3) = 0; eq4 := (cos(beta3)-1)*w12+sin(beta3)*w11+(cos(alpha3)-1)*z12+sin(alpha3)*z11-4*sin(delta3) = 0; eq5 := (cos(beta4)-1)*w11-sin(beta4)*w12+(cos(alpha4)-1)*z11-sin(alpha4)*z12-5*cos(delta4) = 0; eq6 := (cos(beta4)-1)*w12+sin(beta4)*w11+(cos(alpha4)-1)*z12+sin(alpha4)*z11-6*sin(delta4) = 0; eq7 := (cos(beta5)-1)*w11-sin(beta5)*w12+(cos(alpha5)-1)*z11-sin(alpha5)*z12-7*cos(delta5) = 0; eq8 := (cos(beta5)-1)*w12+sin(beta5)*w11+(cos(alpha5)-1)*z12+sin(alpha5)*z11-8*sin(delta5) = 0; alpha2 := -20; alpha3 := -45; alpha4 := -75; alpha5 := -90; delta2 := 15.5; delta3 := -15.9829; delta4 := -13.6018; delta5 := -16.7388; P21 = .5217; P31 = 1.3421; P41 = 2.3116; P51 = 3.1780;

equidistant_curve_MP.mw  Equidistant curves to the curves on the surface. (Without any sense, but real.)







     It is known that ODE boundary value problem is similar to the problem of solving systems of nonlinear equations. Equations are the boundary conditions, and the variables are the values of the initial data.
For example:

y '' = f (x, y, y '), 0 <= x <= 1,

y (0) = Y0, y (1) = Y1;

Where y (1) = Y1 is the equation, and Z0 is variable, (y '(0) = Z0).

     solve () and fsolve () are not directly suitable for such tasks. Directly should work the package of optimization in relation to a system of nonlinear equations. (Perhaps it has already been implemented in Maple.)
Personally, I am very small and unprofessional know Maple and cannot do it. Maybe there is someone who would be interested, and it will try to implement this approach to solving ODE boundary value problems?  

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