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Finite Difference

The document presents a MATLAB code that uses a finite difference method to solve a second order differential equation, with user input for the boundary values and number of intervals. The code sets up and solves a system of equations to calculate the value of y at each interval point, then plots the solution curve and labels the axes.

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106 -Shivam Chahar
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87 views5 pages

Finite Difference

The document presents a MATLAB code that uses a finite difference method to solve a second order differential equation, with user input for the boundary values and number of intervals. The code sets up and solves a system of equations to calculate the value of y at each interval point, then plots the solution curve and labels the axes.

Uploaded by

106 -Shivam Chahar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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clc

Enter the value of lower boundary: 0


clear Enter the value of upper boundary: %pi/2
function [x, y]=secondOrderODE(x1, xn, y1, yn, Enter the value of y(l): 1
n) Enter the value of y(n): 1
h=(xn - x1)/(n -1)
x=linspace(x1,xn,n) "x y"
A=zeros(n-2,n-2)
for i=1:n-3 0. 1.
A(i,i)=h^2 - 2 0.0826735 1.0792224
0.165347 1.1510683
A(i,i + 1)= 1 0.2480205 1.2150469
A(i+1,i)= 1 0.330694 1.2707207
end 0.4133675 1.3177092
0.4960409 1.3556914
A(n-2,n-2)=h^2-2
0.5787144 1.3844075
B=zeros(n-2) 0.6613879 1.4036613
B(1)=-y1 0.7440614 1.4133212
B(n-2)= -yn 0.8267349 1.4133212
0.9094084 1.4036613
y(1)=y1 0.9920819 1.3844075
y(2:n-1)=A\B 1.0747554 1.3556914
y(n)=yn 1.1574289 1.3177092
return; 1.2401024 1.2707207
1.3227759 1.2150469
endfunction 1.4054493 1.1510683
//user input part of the function 1.4881228 1.0792224
disp("Solving second order differential equation 1.5707963 1.
using finite difference method")
n=input("Enter the number of subintervals (N):
");
x1=input("Enter the value of lower boundary: ");
xn=input("Enter the value of upper boundary: ");
y1=input("Enter the value of y(l): ");
yn=input("Enter the value of y(n): ");
[x, y]=secondOrderODE(x1, xn, y1,yn,n);
disp("x y");
disp([x',y]);
plot2d(x,y,2)
title('finite difference method', 'fontsize',5,
'color',2,'edgecol',4,'fontname',5)

xlabel('x axis', 'fontsize',3,'color', 2,'fontname', 3)


ylabel('y axis','fontsize',3,
'color',2,'fontname',5,'rotation',0)
a=gca()
a.box ="on"
a.thickness=1

a.font_size=3

a.font_style=3

a.children.children.thickness=3
xstring(.3, 1.1,"$\frac{d^2y}{dx^2}+y=0:
y(0)=1,y(pi/2)=1$" )

d=get("hdl")

d.font_size=4

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