sql server reporting services barcode font Ordinary Differential Equations in Software

Printer QR Code in Software Ordinary Differential Equations

Ordinary Differential Equations
Decoding QR Code 2d Barcode In None
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
Make QR In None
Using Barcode encoder for Software Control to generate, create QR Code 2d barcode image in Software applications.
d2y + y = 0 with initial conditions y(0) = 0, y'(0) = 1 has a unique solution dx 2 y = sin x. We attempt to solve it for 0 x 10,000.
Recognize QR Code In None
Using Barcode scanner for Software Control to read, scan read, scan image in Software applications.
Make QR Code 2d Barcode In Visual C#.NET
Using Barcode printer for .NET Control to generate, create QR Code image in .NET applications.
EXAMPLE 16 The differential equation
Generating QR Code 2d Barcode In .NET
Using Barcode drawer for ASP.NET Control to generate, create QR image in ASP.NET applications.
QR Code 2d Barcode Creator In Visual Studio .NET
Using Barcode creation for .NET Control to generate, create QR Code ISO/IEC18004 image in .NET framework applications.
equation = NDSolve[{y''[x] + y[x] 0, y[0] 0, y'[0] 1}, y, {x, 0, 10 000}]
Quick Response Code Encoder In Visual Basic .NET
Using Barcode creation for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in Visual Studio .NET applications.
Create UPC-A In None
Using Barcode drawer for Software Control to generate, create GS1 - 12 image in Software applications.
NDSolve mxst : Maximum number of 10000 steps reached at the point x 1422.780656413783`
ECC200 Creator In None
Using Barcode drawer for Software Control to generate, create Data Matrix ECC200 image in Software applications.
Bar Code Maker In None
Using Barcode maker for Software Control to generate, create barcode image in Software applications.
{{y
EAN / UCC - 14 Generation In None
Using Barcode creator for Software Control to generate, create GS1-128 image in Software applications.
EAN / UCC - 13 Maker In None
Using Barcode maker for Software Control to generate, create GTIN - 13 image in Software applications.
InterpolatingFunction[{{0. ,1422.78}}, <>]}}
Bookland EAN Creation In None
Using Barcode creator for Software Control to generate, create ISBN - 10 image in Software applications.
Code-128 Creation In Java
Using Barcode generator for Java Control to generate, create Code 128 Code Set A image in Java applications.
Because of the wide interval, [0, 10000], over which the solution is to be obtained, more than 10,000 steps are necessary.
1D Barcode Printer In Visual Studio .NET
Using Barcode generator for Visual Studio .NET Control to generate, create Linear 1D Barcode image in .NET applications.
Generating EAN13 In Objective-C
Using Barcode generator for iPad Control to generate, create EAN / UCC - 13 image in iPad applications.
equation = NDSolve[{y''[x] + y[x] 0, y[0] 0, y'[0] 1}, y, {x, 0, 10 000}, MaxSteps 100 000] InterpolatingFunction[{{0.,10 000.}},<>]}}
Drawing Bar Code In Visual Studio .NET
Using Barcode encoder for VS .NET Control to generate, create barcode image in .NET framework applications.
European Article Number 13 Encoder In Java
Using Barcode creation for Java Control to generate, create EAN13 image in Java applications.
Having obtained a solution, we check it for accuracy. The solution at x = (4 k + 1) should be 1. 2
Generate European Article Number 13 In Visual C#.NET
Using Barcode generation for .NET Control to generate, create EAN13 image in Visual Studio .NET applications.
UPCA Creation In VB.NET
Using Barcode maker for VS .NET Control to generate, create UPC-A image in VS .NET applications.
f = equation[[1, 1, 2]]; f[633 o/2] 1.00002
SOLVED PROBLEMS
1 dy 11.15 Solve the differential equation = 1 + y 2 = 0, y(0) = 1 , 0 x 1, using DSolve and NDSolve 2 dx and compare the results.
SOLUTION
2 equation1 = DSolve y'[x] 1 + 1 y[x], y[0] 1 , y[x], x 2
Solve ifun : Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information.
y[x] 2 Tan 1 2 x + 2 ArcTan 1 2 2 solution1[x_] = equation1[[1, 1, 2]]; equation2 = NDSolve y'[x] 1 + 1 y[x]2, y[0] 1 ,[y[x],{x,0,1} 2 {{y[x] InterpolatingFunction[{{0., 1.}},<>][x]}} solution2[x_]= equation2[[1, 1, 2]]; tabledata = Table[{x, solution1[x], solution2[x]}, {x,0,1,.1}]; TableForm[tabledata, TableSpacing {1, 15}, TableHeadings {None, {"x","analytic", "numerical"}}]
X 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. analytic 1 1.15817 1.33582 1.53895 1.77601 2.05935 2.40786 2.85196 3.44406 4.28301 5.58016 numerical 1. 1.15817 1.33582 1.53895 1.77601 2.05935 2.40786 2.85196 3.44406 4.28301 5.58016
Ordinary Differential Equations
d 2 y dy dy 11.16 Plot the solution to the differential equation + +1 + y = 0, y(0) = 1, y '(0) = 0 for dt 2 dt dt 0 t 10.
SOLUTION
2 solution1 = NDSolve[y''[t]+(y'[t]+ 1) y'[t] + y[t] 0,y[0] 1, y'[0] 0}, y[t],{t, 0, 10)]
{{y[t]
InterpolatingFunction[{{0.,10.}}, <>][t]}}
Plot[y[t] /. solution,{t, 0, 10}, PlotRange All]
2 0.5
d2y dy 11.17 Plot the (five) solutions to + sin y = 0 for 0 x 30 using initial conditions y'(0) = 0, 2 + 0.3 dx dx y(0) = 2, 1, 0, 1, and 2.
SOLUTION
Do[{solution = NDSolve[{y''[x]+ 0.3 y'[x]+ Sin[y[x]] 0, y[0] i, y'[0] 1}, y[x], {x, 0, 30}];
f[x_]= solution[[1,1,2]];
graph[i]= Plot[f[x], {x, 0, 30}, PlotStyle Hue[.2 i +.5], PlotRange All]}, {i, 2, 2}]; Show[graph[ 2], graph[ 1], graph[0], graph[1], graph[2]]
When plotted in color, the five graphs are clearly distinguishable.
Ordinary Differential Equations
11.3 Laplace Transforms
In this section we describe an ingenious method for solving differential equations. Although the procedure can be used in a wide variety of problems, its real power lies in its ability to solve a differential equation whose right hand side is either discontinuous or zero except on a very short interval when its value is large. Because most of these types of problems arise within the context of time as the independent variable, we will express y and its derivatives as functions of t. We shall discuss Laplace transforms heuristically, and shall not concern ourselves with conditions sufficient for existence. If f is defined on the interval [0, ), the Laplace transform of f(t) is defined L { f (t )} =
e st f (t ) dt
Its usefulness lies in the following properties, which we list without proof: L {1} = 1
L {sinh(bt)} = L {cosh(bt)} =
b s2 b2 s s2 b2 b (s a) 2 b 2 s a (s a ) 2 b 2
L {t } = 1 2
s ! L {t n } = n+1 for positive integers n n s
L {e a t sinh(bt)} = L {e a t cosh(bt)} =
L {e a t} = 1 L {sin(bt)} =
s a b s2 + b2 s s2 + b2 b (s a) 2 + b 2 s a (s a) 2 + b 2
L { f '(t )} = s L { f (t )} f (0) L { f ''(t )} = s 2 L { f (t )} sf (0) f '(0) L {af (t ) + bg(t )} = a L
If F (s) = L
L {cos(bt)} =
L {e a t sin(bt)} = L {e a t cos(bt)} =
{ f (t )} + b L {g(t )}
{ f (t )} , then L {ea t f (t )} = F (s a)
Mathematica computes the Laplace transform of a function, f, by the invocation of the command LaplaceTransform.
LaplaceTransform[f[var1], var1, var2] computes the Laplace transform of the function f, with independent variable var1, and expresses it as a function of var2.
Copyright © OnBarcode.com . All rights reserved.