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docs/ABM_equations_doc.html

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--><title>ABM_equations</title><meta name="generator" content="MATLAB 9.11"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2022-06-05"><meta name="DC.source" content="ABM_equations_doc.m"><style type="text/css">
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</style></head><body><div class="content"><h1><tt>ABM_equations</tt></h1><!--introduction--><p>mth-order Adams-Bashforth-Moulton equations.</p><p><a href="index.html">Back to ODE Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#3">Input/Output Parameters</a></li><li><a href="#4">Example #1: 1st-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#5">Example #2: 2nd-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#6">Example #3: 3rd-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#7">Example #4: 4th-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#8">Example #5: 5th-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#9">Example #6: 6th-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#10">Example #7: 7th-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#11">Example #8: 8th-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#12">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">ABM_equations(m)
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</style></head><body><div class="content"><h1><tt>ABM_equations</tt></h1><!--introduction--><p>mth-order Adams-Bashforth-Moulton equations.</p><p><a href="index.html">Back to IVP Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#3">Input/Output Parameters</a></li><li><a href="#4">Example #1: 1st-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#5">Example #2: 2nd-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#6">Example #3: 3rd-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#7">Example #4: 4th-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#8">Example #5: 5th-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#9">Example #6: 6th-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#10">Example #7: 7th-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#11">Example #8: 8th-order Adams-Bashforth-Moulton equations.</a></li><li><a href="#12">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">ABM_equations(m)
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</pre><h2 id="2">Description</h2><p><tt>ABM_equations(m)</tt> prints the mth-order Adams-Bashforth-Moulton predictor-corrector equations to the Command Window.</p><h2 id="3">Input/Output Parameters</h2><p>
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% mth-order Adams-Bashforth-Moulton equations.
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docs/AB_coefficients_doc.html

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</style></head><body><div class="content"><h1><tt>AB_coefficients</tt></h1><!--introduction--><p>Coefficients for the mth-order Adams-Bashforth predictor.</p><p><a href="index.html">Back to ODE Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#4">Input/Output Parameters</a></li><li><a href="#5">Example #1</a></li><li><a href="#6">Example #2</a></li><li><a href="#7">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">[num,gcd] = AB_coefficients(m)
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</style></head><body><div class="content"><h1><tt>AB_coefficients</tt></h1><!--introduction--><p>Coefficients for the mth-order Adams-Bashforth predictor.</p><p><a href="index.html">Back to IVP Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#4">Input/Output Parameters</a></li><li><a href="#5">Example #1</a></li><li><a href="#6">Example #2</a></li><li><a href="#7">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">[num,gcd] = AB_coefficients(m)
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AB_coefficients(m,<span class="string">'print'</span>)
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</pre><h2 id="2">Description</h2><p><tt>[num,gcd] = AB_coefficients(m)</tt> returns a vector of numerators, <tt>num</tt>, and the greatest common denominator, <tt>gcd</tt>, of the vector <img src="AB_coefficients_doc_eq01200921549956645625.png" alt="$\mathbf{b}=(b_{1},...,b_{m})^{T}$" style="width:76px;height:13px;"> storing the coefficients of the mth-order Adams-Bashforth predictor.</p><p><tt>AB_coefficients(m,'print')</tt> prints the coefficients <img src="AB_coefficients_doc_eq10305764104544354739.png" alt="$b_{1},...,b_{m}$" style="width:39px;height:10px;"> of the mth-order Adams-Bashforth predictor to the Command Window.</p><h2 id="4">Input/Output Parameters</h2><p>
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%% |AB_coefficients|
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docs/AB_predictor_doc.html

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</style></head><body><div class="content"><h1><tt>AB_predictor</tt></h1><!--introduction--><p>mth-order Adams-Bashforth predictor.</p><p><a href="index.html">Back to ODE Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#4">Input/Output Parameters</a></li><li><a href="#5">Example #1: Return a string.</a></li><li><a href="#6">Example #2: 1st-order Adams-Bashforth predictor.</a></li><li><a href="#7">Example #3: 2nd-order Adams-Bashforth predictor.</a></li><li><a href="#8">Example #4: 3rd-order Adams-Bashforth predictor.</a></li><li><a href="#9">Example #5: 4th-order Adams-Bashforth predictor.</a></li><li><a href="#10">Example #6: 5th-order Adams-Bashforth predictor.</a></li><li><a href="#11">Example #7: 6th-order Adams-Bashforth predictor.</a></li><li><a href="#12">Example #8: 7th-order Adams-Bashforth predictor.</a></li><li><a href="#13">Example #9: 8th-order Adams-Bashforth predictor.</a></li><li><a href="#14">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">eqn = AB_predictor(m)
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</style></head><body><div class="content"><h1><tt>AB_predictor</tt></h1><!--introduction--><p>mth-order Adams-Bashforth predictor.</p><p><a href="index.html">Back to IVP Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#4">Input/Output Parameters</a></li><li><a href="#5">Example #1: Return a string.</a></li><li><a href="#6">Example #2: 1st-order Adams-Bashforth predictor.</a></li><li><a href="#7">Example #3: 2nd-order Adams-Bashforth predictor.</a></li><li><a href="#8">Example #4: 3rd-order Adams-Bashforth predictor.</a></li><li><a href="#9">Example #5: 4th-order Adams-Bashforth predictor.</a></li><li><a href="#10">Example #6: 5th-order Adams-Bashforth predictor.</a></li><li><a href="#11">Example #7: 6th-order Adams-Bashforth predictor.</a></li><li><a href="#12">Example #8: 7th-order Adams-Bashforth predictor.</a></li><li><a href="#13">Example #9: 8th-order Adams-Bashforth predictor.</a></li><li><a href="#14">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">eqn = AB_predictor(m)
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</pre><h2 id="2">Description</h2><p><tt>eqn = AB_predictor(m)</tt> returns a string storing the mth-order Adams-Bashforth predictor.</p><p><tt>AB_predictor(m,'print')</tt> prints the mth-order Adams-Bashforth predictor to the Command Window.</p><h2 id="4">Input/Output Parameters</h2><p>
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</style></head><body><div class="content"><h1><tt>AM_coefficients</tt></h1><!--introduction--><p>Coefficients for the mth-order Adams-Moulton corrector.</p><p><a href="index.html">Back to ODE Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#4">Input/Output Parameters</a></li><li><a href="#5">Example #1</a></li><li><a href="#6">Example #2</a></li><li><a href="#7">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">[num,gcd] = AM_coefficients(m)
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</style></head><body><div class="content"><h1><tt>AM_coefficients</tt></h1><!--introduction--><p>Coefficients for the mth-order Adams-Moulton corrector.</p><p><a href="index.html">Back to IVP Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#4">Input/Output Parameters</a></li><li><a href="#5">Example #1</a></li><li><a href="#6">Example #2</a></li><li><a href="#7">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">[num,gcd] = AM_coefficients(m)
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AM_coefficients(m,<span class="string">'print'</span>)
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</pre><h2 id="2">Description</h2><p><tt>[num,gcd] = AM_coefficients(m)</tt> returns a vector of numerators, <tt>num</tt>, and the greatest common denominator, <tt>gcd</tt>, of the vector <img src="AM_coefficients_doc_eq01200921549956645625.png" alt="$\mathbf{b}=(b_{1},...,b_{m})^{T}$" style="width:76px;height:13px;"> storing the coefficients of the mth-order Adams-Moulton corrector.</p><p><tt>AM_coefficients(m,'print')</tt> prints the coefficients <img src="AM_coefficients_doc_eq10305764104544354739.png" alt="$b_{1},...,b_{m}$" style="width:39px;height:10px;"> of the mth-order Adams-Moulton corrector to the Command Window.</p><h2 id="4">Input/Output Parameters</h2><p>
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% Coefficients for the mth-order Adams-Moulton corrector.
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% [num,gcd] = AM_coefficients(m)
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% AM_coefficients(m,'print')
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