Persamaan Diferensial Biasa (Ordinary Differential Equation)

Slides:



Advertisements
Similar presentations
Prof. Muhammad Saeed ( Ordinary Differential Equations )
Advertisements

6/1/ Runge 4 th Order Method Industrial Engineering Majors Authors: Autar Kaw, Charlie Barker
Chapter 6 Differential Equations
SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM Read , 26-2, 27-1 CISE301_Topic8L8&9 KFUPM.
HAMPIRAN NUMERIK SOLUSI PERSAMAAN DIFERENSIAL (lanjutan) Pertemuan 12 Matakuliah: METODE NUMERIK I Tahun: 2008.
Matematika Pertemuan 13 Matakuliah: D0024/Matematika Industri II Tahun : 2008.
Numeriska beräkningar i Naturvetenskap och Teknik 1. Numerical differentiation and quadrature Discrete differentiation and integration Trapezoidal and.
Mechanical Engineering Majors Authors: Autar Kaw, Charlie Barker
5/19/ Runge 4 th Order Method Mechanical Engineering Majors Authors: Autar Kaw, Charlie Barker
18 September 2007 KKKQ 3013 PENGIRAAN BERANGKA Week 11 – Ordinary Differential Equations 18 September am – 9.00 am.
ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 32 Ordinary Differential Equations.
11 September 2007 KKKQ 3013 PENGIRAAN BERANGKA Week 10 – Ordinary Differential Equations 11 September am – 9.00 am.
ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 31 Ordinary Differential Equations.
Initial-Value Problems
Numerical Solutions of Ordinary Differential Equations
Numerical Solution of Ordinary Differential Equation
8/8/ Euler Method Major: All Engineering Majors Authors: Autar Kaw, Charlie Barker
P ROJECT : N UMERICAL S OLUTIONS TO O RDINARY D IFFERENTIAL E QUATIONS IN H ARDWARE Joseph Schneider EE 800 March 30, 2010.
CSE 330 : Numerical Methods Lecture 17: Solution of Ordinary Differential Equations (a) Euler’s Method (b) Runge-Kutta Method Dr. S. M. Lutful Kabir Visiting.
Section 6.1: Euler’s Method. Local Linearity and Differential Equations Slope at (2,0): Tangent line at (2,0): Not a good approximation. Consider smaller.
9/22/ Runge 2 nd Order Method Major: All Engineering Majors Authors: Autar Kaw, Charlie Barker
EE3561_Unit 8Al-Dhaifallah14351 EE 3561 : Computational Methods Unit 8 Solution of Ordinary Differential Equations Lesson 3: Midpoint and Heun’s Predictor.
Computational Method in Chemical Engineering (TKK-2109)
10/20/ Runge 2 nd Order Method Chemical Engineering Majors Authors: Autar Kaw, Charlie Barker
Numerical Integration and Rigid Body Dynamics for Potential Field Planners David Johnson.
5/30/ Runge 4 th Order Method Chemical Engineering Majors Authors: Autar Kaw, Charlie Barker
11/17/ Shooting Method Major: All Engineering Majors Authors: Autar Kaw, Charlie Barker
Integration for physically based animation CSE 3541 Matt Boggus.
1/16/ Runge 4 th Order Method Civil Engineering Majors Authors: Autar Kaw, Charlie Barker
1/19/ Runge 4 th Order Method Major: All Engineering Majors Authors: Autar Kaw, Charlie Barker
Differential Equations Linear Equations with Variable Coefficients.
Today’s class Ordinary Differential Equations Runge-Kutta Methods
Transient. Equation of motion resistance force is proportional to speed : For convenience: Also, k=m  0 2 Trial solution.
2/28/ Runge 4 th Order Method Computer Engineering Majors Authors: Autar Kaw, Charlie Barker
1 6.1 Slope Fields and Euler's Method Objective: Solve differential equations graphically and numerically.
Numerical Integration for physically based animation
Solusi dengan Pendekatan Numerik
Deret Taylor.
ZCE 111 Assignment 11.
Numerical Solution of Ordinary Differential Equation
Advanced Engineering Mathematics, Third Edition
Civil Engineering Majors Authors: Autar Kaw, Charlie Barker
Chemical Engineering Majors Authors: Autar Kaw, Charlie Barker
SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM (Term 101) Section 04 Read , 26-2, 27-1 CISE301_Topic8L4&5.
Section Euler’s Method
First-Order Differential Equations
Sec:25.3 RUNGE-KUTTA METHODS.
Civil Engineering Majors Authors: Autar Kaw, Charlie Barker
Physics 111 Practice Problem Solutions 14 Oscillations SJ 8th Ed
Ordinary differential equaltions:
SHM: Damping Effects Pages
Damped Oscillations.
Industrial Engineering Majors Authors: Autar Kaw, Charlie Barker
ORBITAL Trajectories!!! Made by Karol Sanchez
Scientific Computing Lab
Numerical Solutions of Ordinary Differential Equations
SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM (Term 101) Section 04 Read , 26-2, 27-1 CISE301_Topic8L2.
Numerical Analysis Lecture 38.
Numerical solution of first-order ordinary differential equations
SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM (Term 101) Section 04 Read , 26-2, 27-1 CISE301_Topic8L6.
Chapter 18: Elementary Differential Equations
SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM Read , 26-2, 27-1 CISE301_Topic8L3 KFUPM.
Electrical Engineering Majors Authors: Autar Kaw, Charlie Barker
Numerical Computation and Optimization
Chemical Engineering Majors Authors: Autar Kaw, Charlie Barker
MATH 2140 Numerical Methods
Numerical Analysis Lecture 36.
CISE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM Read , 26-2, 27-1 CISE301_Topic8L7 KFUPM.
Numerical solution of first-order ordinary differential equations 1. First order Runge-Kutta method (Euler’s method) Let’s start with the Taylor series.
CISE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM Read , 26-2, 27-1 CISE301_Topic8L6 KFUPM.
Presentation transcript:

Persamaan Diferensial Biasa (Ordinary Differential Equation)

Deret Taylor

Persamaan Diferensial Biasa (Ordinary Differential Equations) Metode Euler

Graphical depiction of a one step method

Euler’s method

Comparison of two numerical solutions with Euler’s method using step sizes of 0.5 and 0.25.

Persamaan Diferensial Biasa orde 2

MOTION IN THE PRESENCE OF RESISTIVE FORCES Resistive Force Proportional to Object Speed

Contoh Gerak Jatuh dengan Hambatan Solusi eksak Solusi numerik

PD orde 2 DAMPED OSCILLATIONS

ORDINARY DIFFERENTIAL EQUATIONS Runge-Kutta Methods

Second-order Runge-Kutta Methods Third-Order Runge-Kutta Methods

Fourth-Order Runge-Kutta Methods