My Math Forum Runge kutta help!

 Math Software Math Software - Mathematica, Matlab, Calculators, Graphing Software

 February 29th, 2016, 11:16 AM #1 Newbie   Joined: Feb 2016 From: singapore Posts: 1 Thanks: 0 Runge kutta help! how do i use runge kutta on a 2nd order equations? M(d2x/dt2)=Fn(sin θ - uCos θ ) M(d2z/dt2)=Fn(cos θ + uSin θ ) - Mg﻿ i tried Mzdoubledot as shown in the code below, however i dont know how to combine Mzdoubledot with Mxdoubledot. Fn,M,θ,u is constant fn/M = 0.866 clc; % Clears the screen clear all; thete=30; g=9.81; %Constant h=0.1; % step size tfinal = 3; N=ceil(tfinal/h); %y = zeros(1,length(x)); t(1) = 0; % initial condition y(1) = 5; F_zy = @(t,thete) 0.866*(cos(thete)+0.5774*(sin(thete)))-g; F_xy = @(t,thete) 0.866*(sin(thete)-0.5774*(cos(thete))); for i=1:N % calculation loop %update time t(i+1)=t(i)+h; %update motions k_1 = F_xy(t(i),y(i)); k_2 = F_xy(t(i)+0.5*h,y(i)+0.5*h*k_1); k_3 = F_xy((t(i)+0.5*h),(y(i)+0.5*h*k_2)); k_4 = F_xy((t(i)+h),(y(i)+k_3*h)); k_11 = F_zy(t(i),y(i)); k_22 = F_zy(t(i)+0.5*h,y(i)+0.5*h*k_11); k_33 = F_zy((t(i)+0.5*h),(y(i)+0.5*h*k_22)); k_44 = F_zy((t(i)+h),(y(i)+k_33*h)); y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h; y(i+1) = y(i) + (1/6)*(k_11+2*k_22+2*k_33+k_44)*h;% main equation end hold on plot(t,y,'+-', 'Linewidth', 1.5, 'color', 'blue') xlabel('time') ylabel('height') legend('RK4')﻿

 Tags kutta, runge, runge-kutta

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post praveengummadi35 Calculus 0 March 27th, 2014 05:58 PM 0nad Applied Math 1 October 2nd, 2012 10:20 AM thunderkasi Real Analysis 1 October 25th, 2011 04:15 AM UlrichRekenin Calculus 0 August 22nd, 2011 10:54 AM mathmoron Math Software 1 April 8th, 2010 06:35 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top