Computational Mathematics: MATLAB or SciLab - Lab Report Example

Lab Report Logic and Programming Computational mathematics (MATLAB SciLab) Mathematical operations are usually simulated in dynamic languages simulations such as MatLab and SciLab. These software are applications are important in the development of rapid prototypes for technical activities such as Engineering. Development of new mathematical and engineering programs in this project will be developed using SciLab and MatLab. In MatLab program the simulation used is to calculate the calculate the velocity of a moving body, and plotting the graph against time In the SciLab script, the program Table of Contents 1. Introduction This program explores the possibility of simulating mathematical and engineering tasks in programming languages. This study is important as it can enable a mathematician to transform mathematical calculations and operations into relevant form for use in actual working environment (Haidekker 2013, p47). Both Matlab and SciLab display similar results but use different programming syntax (Wouwer, Saucez and Vilas 2014, p52). The choice of which program to use in simulation depends on the programmer’s knowledge and experience. 1.1. Scope This project seeks to compare two programs, one in Matlab and the other in SciLab. It thus contains two scripts in each of the languages along with their outputs. 1.2. Objectives The main aim of this project is to demonstrate the use of programing languages in simulation of mathematical and engineering problem solutions. 2. Methods The method used in this study is quantitative analysis using familiar mathematical and engineering problems and applying the variables and equations in the scripts (Campbell, Chancelier and Nikoukhah 2006, p38). The results are presented in plotted graphs as a summary of the simulated solutions. 2.1. TASK 1 2.1.1. Matlab Script clear all;         %deletion of the former variables  v01 = 0;              %Initial speed dt1 = 0.10;            %Time step t1 = 0: dt: 60;         %Simulation for 10 seconds. g1 = 9.80;             %gravitation force g1 = 0.10;             % coefficient of friction force m1 = 1.0;               %mass - 1 kg. v (1) = v0;           %Setting the initial velocity.  for i1 = 1 : 1 : (length(t1) - 1),     a = g1 - (b / m1) * v1 (i1);    %Calculating the acceleration. v(i1 + 1) = v1(i1) + a * dt1;%Getting the velocity by approximating integration. end  %Exact Solution. Vexact = (m1 * g1 / b) * (1 – exp (-t1 * b / m1)); plot (t1, v1, t1, vexact); legend (Approx velocity,Exact velocity); xlabel (Time); ylabel (Velocity); Output Figure 1: Plotting of Matlab program- Velocity vs Time 2.1.2. SCILAB SCRIPT // Constants DeltaT = 0.01; // 100Hz sample w = (50 / 60) * 2 * %pi; // 50 RPM -> radians persec L = 8/100; // 8 cm -> meters g = 9.81; // Earth gravity in ms^-2 N = 1000; // Number of samples sig_w = 0.00001; sig_v = 1; ww = sig_w * rand(3, N, normal); vv = sig_v * rand(2, N, normal); x = zeros (3, N); x (:,1) = [0, w * DeltaT,0]; z = zeros (2, N); F = [1 1 0; 0 1 1; 0 0 1]; // All nonlinearities are in the output equation function h = output_equation(theta, omega, g, L) h = [g * cos (theta); g * sin (theta) + omega.*omega * L]; endfunction for i=2:N, x(:,i) = F * x(:,i-1) + ww(:,i); if (i>N/4) & (i Read More