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How to implement time dependent heat generation
I leave the rest to you: %% Create thermal model PDE thermalmodel = createpde(1); %% Create Geometry R2= [3,4,-1.5,1.5,1...

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2 eqns in 2D with different BCs applied to each variable on the same edge? On E1, u1=0 and du2/dn=0, on E2 u2=1 and =du1/dn=0. The solution is all zeros. Example code is below
I think applyBoundaryCondition (model, "mixed", Edge=1, u=0, EquationIndex=1,q=[0 0;0 0],g=[0;0]); applyBoundaryCondition (mod...

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Error msg: Undefined function or variable 'optimproblem'. Error in optimize_plant_operation (line 6) prob = optimproblem('ObjectiveSense', 'maximize');
"optimproblem" was introduced in R2017b: https://uk.mathworks.com/help/optim/ug/optimproblem.html at the bottom of the page un...

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Computing velocity with Forward Euler method
@Riccardo Are you sure you can leave temperature fixed with a pressure difference of 12 bar ? And did you try plotting your re...

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model non-autonomous system with neural ode
You can easily convert your non-autonomous system into an autonomous one by defining an additional ODE y2 as dy/dt = y2, y(0...

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Orthotropic Conductivity on Face
I found orthoK = [0.75*kappa; 0.85*kappa]; in the documentation - thus a column instead of a row vector.

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Using fprintf in a for loop to display the output as a set of coordinate points
syms x y real y=x*(4-x)^3;dy=diff(y); x_roots=solve(dy,x); y_x_roots=subs(y,x_roots); for j=1 disp('The critical point(...

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Average Flux Across Edge
Should be averageFlux = 1/(Nodes_Xa(end)-Nodes_Xa(1))*trapz(Nodes_Xa,flux_Xa)

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What do you think of my numerical Jacobian, using the central-difference method?
It cannot be correct because F1,...,F6 are scalars, not functions. And if F1,...,F6 were functions, the 2*h expression must be...

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How should I compute the Jacobian for my equations of motion?
According to your description, at some stage of your procedure, the right-hand side of your ODE system is available as a symboli...

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Trouble animating a double pendulum
theta_1 = 19*pi/180; theta_2 = 30*pi/180; l_1 = 1; l_2 = 1; g = 9.8; m_1 = 1; m_2 = 1; M = m_1 + m_2; dt = .00...

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Numerical Methods for Singular systems
The loop index i does not equal time t. So expressions like d_1=floor(1.5+sin(0.5*i*h)); x1(:,i-d_1-1) x2(:,i-d_1-1) x3(:,i...

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Does anyone know how to use an IF statement with ODE's? I am trying to create an IF statement sigma > 0 , tau > 0 if dx(3,1) > 0, dx(1,1) > 0 and sigma = 0 , tau = 0 otherwise
You mean % linear ODEs dx(1,1) = alpha * y - beta * r * y; dx(3,1) = - theta * w + lambda * y * w - mu * w * w; if dx(1,...

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Integral Recurrence Formula Implementation
This seems to work: xl = 0; xu = 4; q = 12; C1 = 2; vl = (xl*sqrt(xl^2+C1^2)+C1^2*log(xl+sqrt(xl^2+C1^2)))/2; vu = (xu*sqr...

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How to solve a thermal model? NEED HELP!!
Params = load('Params.mat'); S_matrix = load('S_matrix.mat'); MC = Params.MC; Q = Params.Q; S = S_matrix.S; T0 = 298.15; T...

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Apply Dirichlet BC on Vertex
Is there a way to use a function and logic (example below) to have the code use Neumann on edges 1 & 4 but when x=xmax and y=ymi...

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I have a problem with 2D heat conduction develop a computer code to solve the 2D heat conduction equation:∂2T /∂x2 + ∂2T/ ∂y2 = 0, gradient don't change when iterations increase, please help me
The maximum gradient is always in the left and right upper corner point with value (1-0)/(1/40) = 40. So it won't change in the ...

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How to solve a thermal model? NEED HELP!!
I get these curves with your equations and your data. T0 = 298.15; T_air = 293.15; G_air = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 22...

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quadgk AbsTol/RelTol parameters combinations
umin = 1e-16; f = @(t,u) exp(-t*u.^2)./(u.*(besselj(0,u).^2+bessely(0,u).^2)); g = @(u) pi/2 * atan((2*double(eulergamma)-log(...

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Solve not returning values after first iteration?
You overwrite omega3 and omega4 as symbolic variables with numerical values. Replace % Solve the system sol = solve([eq1, eq2...

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BVP unknown parameter 2 column vector
You forgot to include "C_L_aoa" as global variable in the script part of your code. clear all clc close all %%%%%%%%%%%%%%%%...

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Nonlinear Curve fitting with integrals
This code works for your supplied data: Delta = 0.075; delta = 0.002; D = 0.098E-9; gamma = 2.675E8; Rmin = 0.01e-6; Rmax ...

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How to graph coupled differential equations
% Parameters m1 = 4.0; m2 = 6.0; L = 1.5; k = 100.0; % Added missing parameter g = 9.81; F0 = 100; tF = 1; % Initial st...

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Nonlinear Curve fitting with integrals
It takes too long to run the code online - try if it produces reasonable results. Maybe you have to set lower and upper bounds f...

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Matlab function that tells the full path of from where the function has been called
What about passing the full path where the function is located from the respective functions 2,3,4,5... to function1 ? See htt...

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how to deal with discontinuities in solutions to differential equations using ode45
Usually, the differential equations to be solved are much more complicated than yours which makes it impossible to foresee possi...

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How to rename a new matrix obtained by adding a row to the previous matrix
A = [1:5; 6:10] B = [A;11*ones(1,size(A,2))]

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eventfunction for stopping solver when output becomes complex doesn't work
Try options = odeset('Events', @(t,y)stop(t, y, Vb0, lambda, mb, rhog0, Cw)); [t, y] = ode45(@(t, y) DE(t,y, Vb0, lambda, mb,...

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Drawing Bessel function is not possible in that it give me an error
Maybe this is what you want: x=(0:0.01:5).'; i=0:20; hold on for m=0:5 j=sum((-1).^i./(factorial(i).*gamma(i+m+1)).*(x/...

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Facing problems in nonlinear system
"pdepe" gives a different solution than your method. Maybe the nonlinear systems have multiple solutions. %%%% Problem_01 %%%% ...

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