Explicit Euler method

I am looking to find the explicit and implicit codes for Euler's method. In my search I am across the following code, I am wondering if this code is explicit? if not how could I change it to make it so?

import math

# First Order ODE (y' = f(x, y)) Solver using Euler method

# xa: initial value of independent variable

# xb: final value of independent variable

# ya: initial value of dependent variable

# n : number of steps (higher the better)

# Returns value of y at xb.

def Euler(f, xa, xb, ya, n):

      h = (xb - xa) / float(n)

      x = xa

      y = ya

      for i in range(n):

          y += h * f(x, y)

          x += h

      return y

print(Euler(lambda x, y: math.cos(x) + math.sin(y), 0, 1, 1, 1000))

edited Dec 4 '18 at 22:04

Moo

5,53131020

asked Dec 4 '18 at 21:41

user104

1077

add a comment |

import math

# First Order ODE (y' = f(x, y)) Solver using Euler method

# xa: initial value of independent variable

# xb: final value of independent variable

# ya: initial value of dependent variable

# n : number of steps (higher the better)

# Returns value of y at xb.

def Euler(f, xa, xb, ya, n):

      h = (xb - xa) / float(n)

      x = xa

      y = ya

      for i in range(n):

          y += h * f(x, y)

          x += h

      return y

print(Euler(lambda x, y: math.cos(x) + math.sin(y), 0, 1, 1, 1000))

edited Dec 4 '18 at 22:04

Moo

5,53131020

asked Dec 4 '18 at 21:41

user104

1077

add a comment |

import math

# First Order ODE (y' = f(x, y)) Solver using Euler method

# xa: initial value of independent variable

# xb: final value of independent variable

# ya: initial value of dependent variable

# n : number of steps (higher the better)

# Returns value of y at xb.

def Euler(f, xa, xb, ya, n):

      h = (xb - xa) / float(n)

      x = xa

      y = ya

      for i in range(n):

          y += h * f(x, y)

          x += h

      return y

print(Euler(lambda x, y: math.cos(x) + math.sin(y), 0, 1, 1, 1000))

edited Dec 4 '18 at 22:04

Moo

5,53131020

asked Dec 4 '18 at 21:41

user104

1077

import math

# First Order ODE (y' = f(x, y)) Solver using Euler method

# xa: initial value of independent variable

# xb: final value of independent variable

# ya: initial value of dependent variable

# n : number of steps (higher the better)

# Returns value of y at xb.

def Euler(f, xa, xb, ya, n):

      h = (xb - xa) / float(n)

      x = xa

      y = ya

      for i in range(n):

          y += h * f(x, y)

          x += h

      return y

print(Euler(lambda x, y: math.cos(x) + math.sin(y), 0, 1, 1, 1000))

linear-algebra numerical-methods

edited Dec 4 '18 at 22:04

Moo

5,53131020

asked Dec 4 '18 at 21:41

user104

1077

edited Dec 4 '18 at 22:04

Moo

5,53131020

asked Dec 4 '18 at 21:41

user104

1077

edited Dec 4 '18 at 22:04

Moo

5,53131020

edited Dec 4 '18 at 22:04

Moo

5,53131020

edited Dec 4 '18 at 22:04

Moo

5,53131020

asked Dec 4 '18 at 21:41

user104

1077

asked Dec 4 '18 at 21:41

user104

1077

asked Dec 4 '18 at 21:41

user104

1077

add a comment |

1 Answer
1

active

oldest

votes

This code implements the explicit Euler scheme.

In order to be implicit, there would be an instruction like

y = solve(z == y + h*f(x,z), z)

in the inner loop, where solve(equation, variable) is a suitable function to solve an equation (see here).

edited Dec 4 '18 at 21:58

answered Dec 4 '18 at 21:48

Federico

4,829514

how would I add a step size to this code?
– user104
Dec 4 '18 at 21:52

The step size is h, which is currently controlled by the argument n
– Federico
Dec 4 '18 at 21:54

so what do I need to replace that line of code you have in my code?
– user104
Dec 4 '18 at 22:03

You need to implement the code that finds the fixed point in the implicit Euler scheme. You can either use a fixed-point iteration, or a generic nonlinear solver, such as docs.scipy.org/doc/scipy/reference/optimize.html#root-finding
– Federico
Dec 4 '18 at 22:06

either way, thanks for your help!
– user104
Dec 4 '18 at 22:07

add a comment |

Your Answer

StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\$","\$"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});

}
});

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3026217%2fexplicit-euler-method%23new-answer', 'question_page');
}
);

Post as a guest

Name

Required, but never shown

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

This code implements the explicit Euler scheme.

In order to be implicit, there would be an instruction like

y = solve(z == y + h*f(x,z), z)

in the inner loop, where solve(equation, variable) is a suitable function to solve an equation (see here).

edited Dec 4 '18 at 21:58

answered Dec 4 '18 at 21:48

Federico

4,829514

how would I add a step size to this code?
– user104
Dec 4 '18 at 21:52

The step size is h, which is currently controlled by the argument n
– Federico
Dec 4 '18 at 21:54

so what do I need to replace that line of code you have in my code?
– user104
Dec 4 '18 at 22:03

You need to implement the code that finds the fixed point in the implicit Euler scheme. You can either use a fixed-point iteration, or a generic nonlinear solver, such as docs.scipy.org/doc/scipy/reference/optimize.html#root-finding
– Federico
Dec 4 '18 at 22:06

either way, thanks for your help!
– user104
Dec 4 '18 at 22:07

add a comment |

This code implements the explicit Euler scheme.

In order to be implicit, there would be an instruction like

y = solve(z == y + h*f(x,z), z)

in the inner loop, where solve(equation, variable) is a suitable function to solve an equation (see here).

edited Dec 4 '18 at 21:58

answered Dec 4 '18 at 21:48

Federico

4,829514

how would I add a step size to this code?
– user104
Dec 4 '18 at 21:52

The step size is h, which is currently controlled by the argument n
– Federico
Dec 4 '18 at 21:54

so what do I need to replace that line of code you have in my code?
– user104
Dec 4 '18 at 22:03

You need to implement the code that finds the fixed point in the implicit Euler scheme. You can either use a fixed-point iteration, or a generic nonlinear solver, such as docs.scipy.org/doc/scipy/reference/optimize.html#root-finding
– Federico
Dec 4 '18 at 22:06

either way, thanks for your help!
– user104
Dec 4 '18 at 22:07

add a comment |

This code implements the explicit Euler scheme.

In order to be implicit, there would be an instruction like

y = solve(z == y + h*f(x,z), z)

in the inner loop, where solve(equation, variable) is a suitable function to solve an equation (see here).

edited Dec 4 '18 at 21:58

answered Dec 4 '18 at 21:48

Federico

4,829514

This code implements the explicit Euler scheme.

In order to be implicit, there would be an instruction like

y = solve(z == y + h*f(x,z), z)

in the inner loop, where solve(equation, variable) is a suitable function to solve an equation (see here).

edited Dec 4 '18 at 21:58

answered Dec 4 '18 at 21:48

Federico

4,829514

edited Dec 4 '18 at 21:58

answered Dec 4 '18 at 21:48

Federico

4,829514

answered Dec 4 '18 at 21:48

Federico

4,829514

answered Dec 4 '18 at 21:48

Federico

4,829514

how would I add a step size to this code?
– user104
Dec 4 '18 at 21:52

The step size is h, which is currently controlled by the argument n
– Federico
Dec 4 '18 at 21:54

so what do I need to replace that line of code you have in my code?
– user104
Dec 4 '18 at 22:03

You need to implement the code that finds the fixed point in the implicit Euler scheme. You can either use a fixed-point iteration, or a generic nonlinear solver, such as docs.scipy.org/doc/scipy/reference/optimize.html#root-finding
– Federico
Dec 4 '18 at 22:06

either way, thanks for your help!
– user104
Dec 4 '18 at 22:07

add a comment |

how would I add a step size to this code?
– user104
Dec 4 '18 at 21:52

The step size is h, which is currently controlled by the argument n
– Federico
Dec 4 '18 at 21:54

so what do I need to replace that line of code you have in my code?
– user104
Dec 4 '18 at 22:03

You need to implement the code that finds the fixed point in the implicit Euler scheme. You can either use a fixed-point iteration, or a generic nonlinear solver, such as docs.scipy.org/doc/scipy/reference/optimize.html#root-finding
– Federico
Dec 4 '18 at 22:06

either way, thanks for your help!
– user104
Dec 4 '18 at 22:07

how would I add a step size to this code?
– user104
Dec 4 '18 at 21:52

The step size is h, which is currently controlled by the argument n
– Federico
Dec 4 '18 at 21:54

so what do I need to replace that line of code you have in my code?
– user104
Dec 4 '18 at 22:03

You need to implement the code that finds the fixed point in the implicit Euler scheme. You can either use a fixed-point iteration, or a generic nonlinear solver, such as docs.scipy.org/doc/scipy/reference/optimize.html#root-finding
– Federico
Dec 4 '18 at 22:06

either way, thanks for your help!
– user104
Dec 4 '18 at 22:07

add a comment |

draft saved

draft discarded

Thanks for contributing an answer to Mathematics Stack Exchange!

Please be sure to answer the question. Provide details and share your research!

But avoid …

Asking for help, clarification, or responding to other answers.

Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.

To learn more, see our tips on writing great answers.

Some of your past answers have not been well-received, and you're in danger of being blocked from answering.

Please pay close attention to the following guidance:

Please be sure to answer the question. Provide details and share your research!

But avoid …

Asking for help, clarification, or responding to other answers.

Making statements based on opinion; back them up with references or personal experience.

To learn more, see our tips on writing great answers.

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Post as a guest

Name

Required, but never shown

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Name

Required, but never shown

Name

Required, but never shown

This page is only for reference, If you need detailed information, please check here

搜尋此網誌

Htykuut