4th-Order Runge-Kutta Method Example 

May God reward you for all your efforts and all the valuable information that you provide us smoothly .

Omg thanks for giving us code to pass some garbage exam

Masterfully executed!

thanks professor compact and to the point

Do you have any video on Method of Lines?

How can I get the code of 4th-Order Runge-Kutta Method for solving integral equations?

thank you,so simple and usefull

Why does it not display the area under the curve from 0 to xfinal?

what is the alternative function that can be used instead of function handle?

there is only one initial condition as in line 2, but in 12th and 13th line you have used initial conditions x(1)=0 and y(1)=5. why?

Hi sir, i am a under-graduation student there is a code in two file (one is function, another is for output) i am uploading three part one for function , second for output , third for another function where parameter are differents from first one. This code successfully run for first function parameter but not run for third function parameter . please help me. FIRST PART(parameter) function xprime = state1(t,X) % CALCULATE THE TEMPORAL DYNAMICS OF DIFFERENT STATE %__________________________________________________________________ % PARAMETERS USED FOR THE CALCULATION%_____________________________ h = 6.626*10^-34; % Plank's constant (m^2kg/sec) or "Jule" c = 3*10^8; % Speed of light (m/sec^2) lambda_P = 532*10^-9; % wavelength of the pump beam lambda_S = 633*10^-9; % wavelenngth of the signal beam r = 0.5*10^-3; % radius of the pump beam ( 0.5 mm) A = pi*r^2; % Area of the beam E_p = (h*c)/lambda_P; % Pump photon energy (in Jule) E_s = (h*c)/lambda_S; % Signal photon energy (in Jule) %eV = 1.61*10^-19; %E_p_eV = E_p/eV; % Energy of the pump photon in eV %E_s_eV = E_s/eV; % Energy of the laser photon in eV P_p = 1*10^4; % pump power (50 mW) P_s = 32; % signal power (50 mW) sigma_a = (10^-16)*(10^-2)^2; % Absorption cross section (cm^2) sigma_s = (10^-15)*(10^-2)^2; % Emission cross section (cm^2) sigma_TT = (10^-14)*(10^-2)^2; % Triplet-Triplet absorption cross section %sigma_ESA11 = ((10^-16)*(10^-2)^2)/0.001; % Intersystem crossing rate (sec^-1) eta_ISC = 10^8; % Constant intersystem crossing rate sigma_ESA = (10^-14)*(10^-2)^2; %___________________________________________________________ Ip = P_p/(A*E_p); % Pump rate (1/m^2/sce) eta_P = Ip*sigma_a; % Pumping rate (photons/sec) %___________________________________________________________ Is = P_s/(A*E_s); % lasing rate (1/m^2/sce) eta_SE = Is*sigma_s; %___________________________________________________________ t_f = 5*10^-9; % radiative lifetime of the molecules eta_f = 1/t_f; % Rate of spontaneous emission %___________________________________________________________ %eta_ESA = Is*sigma_ESA; %eta_ESA = sigma_ESA; %___________________________________________________________ t_T = 1.5; eta_T = 1/t_T; %______________________________________________ eta_TT = Is*sigma_TT; eta_ESA = Is*sigma_ESA; %______________________________________________________________ %SOLUTION OF ODE BY 4TH ORDER RUNGEE-KUTTA METHOD xprime = [eta_P*X(2)-X(1)*(eta_SE+eta_f+eta_ISC+eta_ESA); -eta_P*X(2)+X(1)*(eta_SE+eta_f)+eta_T*X(3); X(1)*(eta_ISC)-X(3)*(eta_T+eta_TT); eta_TT*X(3); X(1)*eta_ESA]; SECOND PART(ODE Slotuion and plot) S1_0 = 0; S0_0 = 10^32; T1_0 = 0; T2_0 = 0; S2_0 =0; %P_p = 10*10^-3; S_total = S1_0+S0_0+T1_0+T2_0+S2_0; X0 = [S1_0 S0_0 T1_0 T2_0 S2_0]; tspan = [0,100*10^-9]; [t,X] = ode45(@state1,tspan,X0); %plot(t,X) S1 = X(:,1)./S_total; S0 = X(:,2)./S_total; T1 = X(:,3)./S_total; T2 = X(:,4)./S_total; S2 = X(:,5)./S_total; %_______________________________________ %Laser intensity calculation through Population inversion" L = (S1-S0); Norm_L = L/max(L); plot(t,S1,'-r'); hold on plot(t,S0,'-g'); hold on plot(t,T1,'-b'); hold on plot(t,T2,'-*'); hold on plot(t,Norm_L, '--r'); hold on plot(t,S2, '-y') ylim ([0 1]); FIRST PART(For different parameter for which code not run) function xprime = state1(t,X) % CALCULATE THE TEMPORAL DYNAMICS OF DIFFERENT STATE %__________________________________________________________________ % PARAMETERS USED FOR THE CALCULATION%_____________________________ h = 6.626*10^-34; % Plank's constant (m^2kg/sec) or "Jule" c = 3*10^8; % Speed of light (m/sec^2) lambda_P = 556*10^-9; % wavelength of the pump beam lambda_S = 626*10^-9; % wavelenngth of the signal beam r = 0.2*10^-3; % radius of the pump beam ( 0.5 mm) A = pi*r^2; % Area of the beam E_p = (h*c)/lambda_P; % Pump photon energy (in Jule) E_s = (h*c)/lambda_S; % Signal photon energy (in Jule) %eV = 1.61*10^-19; %E_p_eV = E_p/eV; % Energy of the pump photon in eV %E_s_eV = E_s/eV; % Energy of the laser photon in eV P_p = 1*10^4; % pump power (50 mW) P_s = 32; % signal power (50 mW) sigma_a = 1.8*10^-24; % Absorption cross section (cm^2) sigma_s = 9*10^-18; % Emission cross section (cm^2) sigma_TT = .1*10^-12; % Triplet-Triplet absorption cross section %sigma_ESA11 = ((10^-16)*(10^-2)^2)/0.001; % Intersystem crossing rate (sec^-1) eta_ISC = 4.2*10^5; % Constant intersystem crossing rate sigma_ESA = (10^-14)*(10^-2)^2; %___________________________________________________________ Ip = P_p/(A*E_p); % Pump rate (1/m^2/sce) eta_P = Ip*sigma_a; % Pumping rate (photons/sec) %___________________________________________________________ Is = P_s/(A*E_s); % lasing rate (1/m^2/sce) eta_SE = Is*sigma_s; %___________________________________________________________ t_f = 350*10^-12; % radiative lifetime of the molecules eta_f = 1/t_f; % Rate of spontaneous emission %___________________________________________________________ %eta_ESA = Is*sigma_ESA; %eta_ESA = sigma_ESA; %___________________________________________________________ t_T = 10^-3; eta_T = 1/t_T; %______________________________________________ eta_TT = Is*sigma_TT; eta_ESA = Is*sigma_ESA; %______________________________________________________________ %SOLUTION OF ODE BY 4TH ORDER RUNGEE-KUTTA METHOD xprime = [eta_P*X(2)-X(1)*(eta_SE+eta_f+eta_ISC+eta_ESA); -eta_P*X(2)+X(1)*(eta_SE+eta_f)+eta_T*X(3); X(1)*(eta_ISC)-X(3)*(eta_T+eta_TT); eta_TT*X(3); X(1)*eta_ESA]; May be problem occurs in this line [t,X] = ode45(@state1,tspan,X0); How i can solve this.

how can you use this program without using the step size method

Hello, I had a problem over here in MATLAB code for solving a linear first ode dx/dt= lambda-sigma*x(t)- c*v(t),dv/dt=k*v(t)-a*z(t),dz/dt=h*x(t)-tow*v(t) with initial conditions x(0)= x0,v(0)=v0,z(0)=x0."Can u help me out sir...

Thank you Professor

l = 120; %cm s = 80; % cm% R = 2*l/s; %l=connecting rod length % s is stroke d= 6.7 %cm Vd = (pi/4)*(d^2)*s; % d is bore % s is stroke a_1 = (R^2 - (sind(theta))^2)^-0.5; dV= (Vd/2)*sind(theta)*(1+(cosd(theta)*a_1)) Sir, i want to solve above equation dV with respect to theta usuing RK4 method in matlab plz help me

can you provide the matlab code for differential quadrature method with RK4 method

How can we know the governing function of the plot?

i am trying to use runge kutta on the lorentz force. do you have nay advice?

I think it will be better to zoom certain areas in your screen it very difficult to see.... but, I like the English, is clear.... just the visual

Can you give this Matlab code?

Nice video :)

i m really confused how to use this method Runge Kutta with Matlab for My code using the analytical methode and Tlm method this my code how i m gonna choose y for this please if you can help to solve it % RC in series TLM application - 2nd edition clear all clc % Vs=input('Source Voltage in Volt ='); Vs=2.7; % R=input('Resistance in ohm ='); R=1; %C=input('Capacitance in Farad ='); C=50; % t=input('Enter The Simulation Time ='); t=300; % dt=input('Time step in second ='); dt= 50; disp('Characteristic Impedance') Zc=dt/(2*C) % k=0 V0c=0; I0=Vs/R; V0ci=-(I0*Zc)/2; V0cr=V0c-V0ci; n=t/dt; for k=1:n Vci(k)=V0cr; I(k)=(Vs-2*Vci(k))/(R+Zc); Vc(k)=2*Vci(k)+I(k)*Zc; Vcr(k)=Vc(k)-Vci(k); V0cr=Vcr(k); % update end %Analytical value of I(t) x=1; for k=0:dt:t i(x)=(Vs/R)*exp(-k/(R*C)); x=x+1; end % Outcomes I=[I0 I]; Vc=[V0c Vc]; Vci=[V0ci Vci]; Vcr=[(V0c-V0ci) Vcr]; t=0:dt:t; plot(t,I),grid,hold,ylabel('magnitude'),xlabel('time in Sec.') plot(t,i,'r') legend('TLM Method','Analytical Method'); % Error Analysis ll=length(i); for k=1:ll err(k)=100*((i(k)-I(k))/i(k)); end disp('Errors in Percent') err;

for this function, how we can resolve it : f^4 - f*f^3 + 4*g*g^1

i need to find a numerical result, what should i have to add?

with matlab

Can you give this Matlab code?