Explanation Given: S ( 0 ) = 1 S ( 1 ) = 3 S ( 2 ) = 3 S ( 3 ) = 4 S ( 4 ) = 2 S ' ' = ( 0 ) = 3 , S ' ' ( 4 ) = 2 Formula used: The cubic spline is give by S i ( x ) = a i + b i ( x − x i ) + c i ( x − x i ) 2 + d i ( x − x i ) 3 Calculation: Now we are going to use the MATLAB commands to plot the cubic spline. Now consider the matlab program splinecoeff A ( 1 , 1 ) = 2 ; r ( 1 ) = v 1 ; A ( n , n ) = 2 ; r ( n ) = v n ; v n = 2 ; v 1 = 3 Matlab program: Clear all; Clc; From the given data, Let x = [ 0 1 2 3 4] y=[1 3 3 4 2] Use the command s p l i n e c o e f f ( x , y ) ; Then we get following values. [ b 1 c 1 d 1 b 2 c 2 d 2 b 3 c 3 d 3 b 4 c 4 d 4 ] = [ 1

3rd Edition

ISBN: 9780134696454

Author: Sauer, Tim

Publisher: Pearson,

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Differential Equations

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Chapter 3.4, Problem 4CP

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Chapter 3 Solutions

Numerical Analysis

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The equations and to plot the cubic spline S that satisfying the given data.

Solution Summary: The author explains how to plot the cubic spline using MATLAB commands.

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To find: The equations and to plot the cubic spline S that satisfying the given data.

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Chapter 3 Solutions