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Problem 1031. Composite Trapezoidal Rule for Numeric Integration

Solution 162795

Submitted on 16 Nov 2012 by Richard Zapor
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Test Suite

Test Status Code Input and Output
1   Pass
%% Simple Trapezoidal Rule p=[2 0 -4 0 -1 1]; a=-2; b=4; f = @(x) polyval(p,x); assert(isequal(trapezoidal_rule(f,a,b,1),5280))

2   Pass
%% Composite Trapezoidal Rule for 2 intervals p=[2 0 -4 0 -1 1]; a=-2; b=4; f = @(x) polyval(p,x); assert(isequal(trapezoidal_rule(f,a,b,2),2634))

3   Pass
%% Composite Trapezoidal Rule for 4 intervals p=[2 0 -4 0 -1 1]; a=-2; b=4; f = @(x) polyval(p,x); assert(isequal(trapezoidal_rule(f,a,b,4),1516.875))

4   Pass
%% Exact analytical comparison p=[2 0 -4 0 -1 1]; a=-2; b=4; f = @(x) polyval(p,x); P=polyint(p); I_correct=polyval(P,b)-polyval(P,a); I=trapezoidal_rule(f,a,b); assert(abs(I-I_correct)<1)

5   Pass
%% Exact analytical comparison--higher tolerance p=[2 0 -4 0 -1 1]; a=-2; b=4; f = @(x) polyval(p,x); I = trapezoidal_rule(f,a,b,1000); P=polyint(p); I_correct=polyval(P,b)-polyval(P,a); assert(abs(trapezoidal_rule(f,a,b,1000)-I_correct)<1e-1)

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