Differential equations - Revision history

A WASSERMANN at 08:46, 18 December 2020

2020-12-18T08:46:40Z

← Older revision		Revision as of 08:46, 18 December 2020
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	var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});		var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});
	var slider = brd.create('slider',[[-7,8],[7,8],[-15,0,15]], {name:'c'});		var slider = brd.create('slider',[[-7,8],[7,8],[-15,0,15]], {name:'c'});
	var P = brd.create('point',[0,1], {name:'(~~x_0~~, y_0)'});		var P = brd.create('point',[0,1], {name:'(t_0, y_0)'});
	var f;		var f;

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	* [[Autocatalytic process]]		* [[Autocatalytic process]]
	* [[Logistic process]]		* [[Logistic process]]
	* Paul Pearson has written a very nice variation: [http://faculty.fortlewis.edu/Pearson_P/jsxgraph/slopefield.html Slope fields and solution curves (using the Runge-Kutta)]

	===The underlying JavaScript code===		===The underlying JavaScript code===
	<source lang="xml">		<source lang="xml">
	<form>		<form>
	f(x,y)=<input type="text" id="odeinput" value="(2-t)*y + c"><input type=button value="ok" onclick="doIt()">		f(t,y)=<input type="text" id="odeinput" value="(2-t)*y + c"><input type=button value="ok" onclick="doIt()">
	</form>		</form>
	</source>		</source>
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	var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});		var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});
	var slider = brd.create('slider',[[-7,8],[7,8],[-15,0,15]], {name:'c'});		var slider = brd.create('slider',[[-7,8],[7,8],[-15,0,15]], {name:'c'});
	var P = brd.create('point',[0,1], {name:'(~~x_0~~, y_0)'});		var P = brd.create('point',[0,1], {name:'(t_0, y_0)'});
	var f;		var f;

	function doIt() {		function doIt() {
	var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 'x, y');		var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 't, y');
	f = function (x, yy) {		f = function (t, yy) {
	return [snip(x, yy[0])];		return [snip(t, yy[0])];
	}		}
	brd.update();		brd.update();

A WASSERMANN at 08:41, 18 December 2020

2020-12-18T08:41:45Z

← Older revision		Revision as of 08:41, 18 December 2020
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	Display solutions of the ordinary differential equation		Display solutions of the ordinary differential equation
	:<math> y'= f(t,y)</math>		:<math> y'= f(t,y)</math>
	with initial value <math>(~~x_0~~,y_0)</math>.		with initial value <math>(t_0,y_0)</math>.

	It is easy to incorporate sliders: give the slider a (unique) name and use this name in the equation. In the example below, the slider name is <math>c</math>.		It is easy to incorporate sliders: give the slider a (unique) name and use this name in the equation. In the example below, the slider name is <math>c</math>.
	<html>		<html>
	<form>		<form>
	f(x,y)=<input type="text" id="odeinput" value="(2-x)*y + c"><input type=button value="ok" onclick="doIt()">		f(t,y)=<input type="text" id="odeinput" value="(2-t)*y + c"><input type=button value="ok" onclick="doIt()">
	</form>		</form>
	</html>		</html>
Line 17:		Line 17:

	function doIt() {		function doIt() {
	var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 'x, y');		var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 't, y');
	f = function (x, yy) {		f = function (t, yy) {
	return [snip(x, yy[0])];		return [snip(t, yy[0])];
	}		}
	brd.update();		brd.update();
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	<source lang="xml">		<source lang="xml">
	<form>		<form>
	f(x,y)=<input type="text" id="odeinput" value="(2-x)*y + c"><input type=button value="ok" onclick="doIt()">		f(x,y)=<input type="text" id="odeinput" value="(2-t)*y + c"><input type=button value="ok" onclick="doIt()">
	</form>		</form>
	</source>		</source>

A WASSERMANN at 11:39, 19 January 2017

2017-01-19T11:39:25Z

← Older revision		Revision as of 11:39, 19 January 2017
Line 55:		Line 55:
	<source lang="xml">		<source lang="xml">
	<form>		<form>
	f(x,y)=<input type="text" id="odeinput" value="(2-x)*y"><input type=button value="ok" onclick="doIt()">		f(x,y)=<input type="text" id="odeinput" value="(2-x)*y + c"><input type=button value="ok" onclick="doIt()">
	</form>		</form>
	</source>		</source>

A WASSERMANN at 11:38, 19 January 2017

2017-01-19T11:38:50Z

← Older revision		Revision as of 11:38, 19 January 2017
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	:<math> y'= f(t,y)</math>		:<math> y'= f(t,y)</math>
	with initial value <math>(x_0,y_0)</math>.		with initial value <math>(x_0,y_0)</math>.

			It is easy to incorporate sliders: give the slider a (unique) name and use this name in the equation. In the example below, the slider name is <math>c</math>.
	<html>		<html>
	<form>		<form>

A WASSERMANN at 11:37, 19 January 2017

2017-01-19T11:37:20Z

← Older revision		Revision as of 11:37, 19 January 2017
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	<html>		<html>
	<form>		<form>
	f(x,y)=<input type="text" id="odeinput" value="(2-x)*y"><input type=button value="ok" onclick="doIt()">		f(x,y)=<input type="text" id="odeinput" value="(2-x)*y + c"><input type=button value="ok" onclick="doIt()">
	</form>		</form>
	</html>		</html>
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	var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});		var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});
	var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});		var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});
	var slider = brd.create('slider',[[-7,8],[7,8],[-15,10,15]], {name:'c'});		var slider = brd.create('slider',[[-7,8],[7,8],[-15,0,15]], {name:'c'});
	var P = brd.create('point',[0,1], {name:'(x_0, y_0)'});		var P = brd.create('point',[0,1], {name:'(x_0, y_0)'});
	var f;		var f;
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	var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});		var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});
	var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});		var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});
			var slider = brd.create('slider',[[-7,8],[7,8],[-15,0,15]], {name:'c'});
	var P = brd.create('point',[0,1], {name:'(x_0, y_0)'});		var P = brd.create('point',[0,1], {name:'(x_0, y_0)'});
	var f;		var f;
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	}		}
	};		};
	doIt();</source>		doIt();
			</source>

	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Calculus]]		[[Category:Calculus]]

A WASSERMANN at 11:36, 19 January 2017

2017-01-19T11:36:25Z

← Older revision		Revision as of 11:36, 19 January 2017
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	var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});		var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});
	var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});		var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});
	var slider = brd.create('slider',[[-7,~~9.5~~],[7,~~9.5~~],[-15,10,15]], {name:'c'});		var slider = brd.create('slider',[[-7,8],[7,8],[-15,10,15]], {name:'c'});
	var P = brd.create('point',[0,1], {name:'(x_0, y_0)'});		var P = brd.create('point',[0,1], {name:'(x_0, y_0)'});
	var f;		var f;

A WASSERMANN at 11:36, 19 January 2017

2017-01-19T11:36:04Z

← Older revision		Revision as of 11:36, 19 January 2017
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	var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});		var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});
	var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});		var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});
			var slider = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'c'});
	var P = brd.create('point',[0,1], {name:'(x_0, y_0)'});		var P = brd.create('point',[0,1], {name:'(x_0, y_0)'});
	var f;		var f;

A WASSERMANN at 11:27, 19 January 2017

2017-01-19T11:27:11Z

← Older revision		Revision as of 11:27, 19 January 2017
Line 1:		Line 1:
	Display solutions of the ordinary differential equation		Display solutions of the ordinary differential equation
	:<math> y'= f(x,y)</math>		:<math> y'= f(t,y)</math>
	with initial value <math>(x_0,y_0)</math>.		with initial value <math>(x_0,y_0)</math>.
	<html>		<html>
Line 58:		Line 58:
	var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});		var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});
	var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});		var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});
	var P = brd.create('point',[0,1], {name:'(x_0,y_0)'});		var P = brd.create('point',[0,1], {name:'(x_0, y_0)'});
			var f;

	function doIt() {		function doIt() {
	var ~~txt~~ = ~~JXG~~.~~GeonextParser~~.~~geonext2JS~~(document.getElementById("odeinput").value);		var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 'x, y');
	f = ~~new Function~~("x", "yy", ~~"var y =~~ yy[0]~~; var z = " + txt + "; return [z~~]");		f = function (x, yy) {
			return [snip(x, yy[0])];
			}
	brd.update();		brd.update();
	}		}
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	var data = ode();		var data = ode();
	var h = N.Value()/200;		var h = N.Value()/200;
			var i;
	this.dataX = [];		this.dataX = [];
	this.dataY = [];		this.dataY = [];
	for(~~var~~ i=0; i<data.length; i++) {		for(i=0; i<data.length; i++) {
	this.dataX[i] = P.X()+i*h;		this.dataX[i] = P.X()+i*h;
	this.dataY[i] = data[i][0];		this.dataY[i] = data[i][0];
	}		}
	};		};
	doIt();		doIt();</source>
	</source>

	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Calculus]]		[[Category:Calculus]]

A WASSERMANN at 11:25, 19 January 2017

2017-01-19T11:25:49Z

← Older revision		Revision as of 11:25, 19 January 2017
Line 16:		Line 16:
	var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 'x, y');		var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 'x, y');
	f = function (x, yy) {		f = function (x, yy) {
	return [snip(yy[0~~], yy[1~~])];		return [snip(x, yy[0])];
	}		}
	brd.update();		brd.update();

A WASSERMANN at 11:24, 19 January 2017

2017-01-19T11:24:04Z

← Older revision		Revision as of 11:24, 19 January 2017
Line 16:		Line 16:
	var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 'x, y');		var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 'x, y');
	f = function (x, yy) {		f = function (x, yy) {
	return [~~snip1~~(yy[0], yy[1])];		return [snip(yy[0], yy[1])];
	}		}
	brd.update();		brd.update();