featL Adding code appendix, god bless america:

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PolishPigeon 2022-01-09 21:39:38 +01:00
parent f9c270a61c
commit 68fc735987
14 changed files with 2279 additions and 2370 deletions

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Chapter 2.
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@ -1,16 +0,0 @@
\BOOKMARK [0][-]{chapter.1}{Determine polynomial function fitting experimental data}{}% 1
\BOOKMARK [1][-]{section.1.1}{Problem}{chapter.1}% 2
\BOOKMARK [1][-]{section.1.2}{Theoretical introduction}{chapter.1}% 3
\BOOKMARK [2][-]{subsection.1.2.1}{Linear Least Squares Problem}{section.1.2}% 4
\BOOKMARK [2][-]{subsection.1.2.2}{Gram matrix and QR decomposition}{section.1.2}% 5
\BOOKMARK [2][-]{subsection.1.2.3}{Gram-Schmidt algorithm}{section.1.2}% 6
\BOOKMARK [1][-]{section.1.3}{Results}{chapter.1}% 7
\BOOKMARK [0][-]{chapter.2}{Determine trajectory of the motion}{}% 8
\BOOKMARK [1][-]{section.2.1}{a\) Runge-Kutta method of 4th order and Adams PC}{chapter.2}% 9
\BOOKMARK [2][-]{subsection.2.1.1}{Problem}{section.2.1}% 10
\BOOKMARK [2][-]{subsection.2.1.2}{Theoretical Introdution}{section.2.1}% 11
\BOOKMARK [2][-]{subsection.2.1.3}{Adams PC method}{section.2.1}% 12
\BOOKMARK [1][-]{section.2.2}{b\) Runge-Kutta method of 4th order with variable step size automatically adjusted}{chapter.2}% 13
\BOOKMARK [2][-]{subsection.2.2.1}{Problem}{section.2.2}% 14
\BOOKMARK [2][-]{subsection.2.2.2}{Theoretical Introdution}{section.2.2}% 15
\BOOKMARK [1][-]{section.2.3}{Results}{chapter.2}% 16

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@ -1,19 +0,0 @@
\contentsline {chapter}{\numberline {1}Determine polynomial function fitting experimental data}{2}{chapter.1}%
\contentsline {section}{\numberline {1.1}Problem}{2}{section.1.1}%
\contentsline {section}{\numberline {1.2}Theoretical introduction}{3}{section.1.2}%
\contentsline {subsection}{\numberline {1.2.1}Linear Least Squares Problem}{3}{subsection.1.2.1}%
\contentsline {subsection}{\numberline {1.2.2}Gram matrix and QR decomposition}{3}{subsection.1.2.2}%
\contentsline {subsection}{\numberline {1.2.3}Gram-Schmidt algorithm}{4}{subsection.1.2.3}%
\contentsline {section}{\numberline {1.3}Results}{5}{section.1.3}%
\contentsline {chapter}{\numberline {2}Determine trajectory of the motion}{12}{chapter.2}%
\contentsline {section}{\numberline {2.1}a) Runge-Kutta method of $4^{th}$ order and Adams PC}{12}{section.2.1}%
\contentsline {subsection}{\numberline {2.1.1}Problem}{12}{subsection.2.1.1}%
\contentsline {subsection}{\numberline {2.1.2}Theoretical Introdution}{12}{subsection.2.1.2}%
\contentsline {subsubsection}{Runge-Kutta method of order 4}{13}{section*.2}%
\contentsline {subsection}{\numberline {2.1.3}Adams PC method}{13}{subsection.2.1.3}%
\contentsline {section}{\numberline {2.2}b) Runge-Kutta method of $4^{th}$ order with variable step size automatically adjusted}{14}{section.2.2}%
\contentsline {subsection}{\numberline {2.2.1}Problem}{14}{subsection.2.2.1}%
\contentsline {subsection}{\numberline {2.2.2}Theoretical Introdution}{14}{subsection.2.2.2}%
\contentsline {subsubsection}{Error estimation using step doubling-approach}{14}{section*.3}%
\contentsline {subsubsection}{Actual correction of the step size}{16}{section*.4}%
\contentsline {section}{\numberline {2.3}Results}{17}{section.2.3}%

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@ -36,7 +36,6 @@ end
function [x, derivativesTable] = rk4stepLoop(x, step, equations, stepSize, derivativesTable)
stepValue = x(:, step);
[x, derivativesTable] = equationsLoop(x, equations, stepValue, stepSize, step, derivativesTable);
end
function [x, derivativesTable] = equationsLoop(x, equations, stepValue, stepSize, step, derivativesTable)

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@ -42,7 +42,6 @@ function [stepSize, errors] = calculateStepAndErrors(equations, stepValue, stepS
stepValue = calculateNextStep(equations, stepValue, stepSize);
[stepCorrectionFactor, errors] = calculateStepCorrection(stepValue, x, step, relativeEpsilon, absoluteEpsilon, errors);
stepSize = 0.9 * stepCorrectionFactor * stepSize;
end
function [step, stepValue] = initializeSteps(step, x)

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@ -6,7 +6,6 @@ function task1(polynomialDegree)
displayInfo(currentPolynomialDegree, error, conditionNumber);
plotGraph(currentPolynomialDegree, dataPoints, LSPSolutions)
end
end
function displayInfo(currentPolynomialDegree, error, conditionNumber)
@ -72,7 +71,6 @@ end
function arrayOfValues = valueApproximationAtx(LSPSolutions, arrayOfArguments)
arrayOfValues = zeros(1, size(arrayOfArguments, 2));
arrayOfValues = calculateArrayofValues(arrayOfArguments, arrayOfValues, LSPSolutions);
end
function arrayOfValues = calculateArrayofValues(arrayOfArguments, arrayOfValues, LSPSolutions)