Euler's Method is used to approximate solutions to differential equations. The document provides two examples:
1) Approximating y(2) given dy/dx = 2x + y, y(1) = -3, using two steps of size 0.5. The approximation is y(2) ≈ -3.75.
2) Approximating y(4) given dy/dx = y - 2, y(0)=4, using four steps of size 1. The approximation is y(4) ≈ 34.
These slides contain information about Euler method,Improved Euler and Runge-kutta's method.How these methods are helpful and applied to our questions are detailed discussed in the slides.
These slides contain information about Euler method,Improved Euler and Runge-kutta's method.How these methods are helpful and applied to our questions are detailed discussed in the slides.
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Here i have given some topics which is related to numerical method and computing.I covered picards method, Taylors series method, Curve fitting of method of least square and fitting a non leaner curve.
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IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
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Please send comments and suggestions for improvements to solo.hermelin@gmail.com. Thanks.
More presentations on different subjects can be found on my website at http://www.solohermelin.com.
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Numerical method-Picards,Taylor and Curve Fitting.Keshav Sahu
Here i have given some topics which is related to numerical method and computing.I covered picards method, Taylors series method, Curve fitting of method of least square and fitting a non leaner curve.
Derivation and solution of the heat equation in 1-DIJESM JOURNAL
Heat flows in the direction of decreasing temperature, that is, from hot to cool. In this paper we derive the heat equation and consider the flow of heat along a metal rod. The rod allows us to consider the temperature, u(x,t), as one dimensional in x but changing in time, t.
Numerical Solution of Diffusion Equation by Finite Difference Methodiosrjce
IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
LINEAR DIFFERENTIAL EQUATION & BERNOULLI`S EQUATIONTouhidul Shawan
This slide is about LINEAR DIFFERENTIAL EQUATION & BERNOULLI`S EQUATION. It is one of the important parts of mathematics. This slide will help you to understand the basis of these two parts one Linear Differential Equation and other Bernoulli`s equation.
Gamma Function mathematics and history.
Please send comments and suggestions for improvements to solo.hermelin@gmail.com. Thanks.
More presentations on different subjects can be found on my website at http://www.solohermelin.com.
Dealing with Notations and conventions in tensor analysis-Einstein's summation convention covariant and contravariant and mixed tensors-algebraic operations in tensor symmetric and skew symmetric tensors-tensor calculus-Christoffel symbols-kinematics in Riemann space-Riemann-Christoffel tensor.
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2. Given that y(1) = -3 and
𝑑𝑦
𝑑𝑥
= 2𝑥 + 𝑦, approximate y(2)
using Euler’s Method and two steps of equal size.
Since we have to get from x = 1 to x = 2 using two steps of equal size, our
step-size will be 0.5.
𝑥0 = 1
𝑦0 = −3
~~~~~~~~~~
𝑥1 = 1 + 0.5 = 1.5
𝑦1 = −3 + 0.5 2 1 − 3 = −3 + 0.5 −1 = −3.5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
𝑥2 = 1.5 + 0.5 = 2
𝑦2 = −3.5 + 0.5 2 1.5 + −3.5 = −3.5 + 0.5 −0.5 = −3.75
So, 𝒚 𝟐 ≈ −𝟑. 𝟕𝟓.
3. Consider
𝑑𝑦
𝑑𝑥
= 𝑦 − 2, where y(0)=4. Use Euler’s Method with
4 equal subintervals to approximate y(4).
Since we have to get from x = 0 to x = 4 using four steps of equal size, our step-size will be 1.
𝑥0 = 0
𝑦0 = 4
~~~~~~~~~~
𝑥1 = 0 + 1 = 1
𝑦1 = 4 + 1 4 − 2 = 4 + 2 = 6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
𝑥2 = 1 + 1 = 2
𝑦2 = 6 + 1 6 − 2 = 6 + 4 = 10
~~~~~~~~~~~~~~~~~~~~~~~~
𝑥3 = 2 + 1 = 3
𝑦3 = 10 + 1 10 − 2 = 10 + 8 = 18
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
𝑥4 = 3 + 1 = 4
𝑦4 = 18 + 1 18 − 2 = 18 + 16 = 34
So, 𝒚 𝟒 ≈ 𝟑𝟒.
