Problem 51322. Solve an ODE: diffusion problem 1

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Problem</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>In the solution of a problem involving diffusion, the following ordinary differential equation arises</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"f''+a eta f' = 0\"/></w:customXmlPr><w:r><w:t>f\\prime\\prime + a\\eta f\\prime = 0</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>where </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"a\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:t> is a positive constant and primes denote differentiation with respect to the independent variable </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"eta\"/></w:customXmlPr><w:r><w:t>\\eta</w:t></w:r></w:customXml><w:r><w:t>. The problem has the conditions </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"f(0) = f0\"/></w:customXmlPr><w:r><w:t>f(0) = f_0</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"f(infinity) = 0\"/></w:customXmlPr><w:r><w:t>f(\\infty ) = 0</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function to solve this problem—that is, return values of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>f</w:t></w:r></w:customXml><w:r><w:t> at specified values of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"eta\"/></w:customXmlPr><w:r><w:t>\\eta</w:t></w:r></w:customXml><w:r><w:t>. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Background</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The physical problem involves diffusion of a quantity from one point where the concentration is maintained at a constant value into a medium in which the concentration is zero far away. The ODE results from transforming the diffusion equation—a partial differential equation in time and a spatial coordinate—with a similarity solution. </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 264.25px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 132.125px; transform-origin: 407px 132.125px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28px 7.91667px; transform-origin: 28px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Problem</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 295.017px 7.91667px; transform-origin: 295.017px 7.91667px; unicode-bidi: normal; "><span style="">In the solution of a problem involving diffusion, the following ordinary differential equation arises</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="f''+a eta f' = 0" style="width: 91px; height: 18px;" width="91" height="18"></span></div><div style="block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; "><span style="">where </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">a</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 298.233px 7.91667px; transform-origin: 298.233px 7.91667px; unicode-bidi: normal; "><span style=""> is a positive constant and primes denote differentiation with respect to the independent variable </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">η</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.1167px 7.91667px; transform-origin: 45.1167px 7.91667px; unicode-bidi: normal; "><span style="">. The problem has the conditions </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHgAAAAoCAYAAAA16j4lAAAD1UlEQVR4nO1af5HzIBB9HuKgBmKgCk5BHcRBHdRCNVRCPdRCNNRCvz/gTfbypbsLgaa54c1kbpojLPD2JwA0NDQ0NDQ0NDR8NQ4AjonfdACu8W+pMVwK9veN6OPzUYEjgDsCWU8Ag+O7Ln5jDfYA4ATgHB+r/RHAA3+P5BPC2l4R1m1EukEl4wjgBeAWfw/x9xP6AncIJGgDpHW/Yr9HTJO8QSf6FPv/KzhjWgcgzP+FQHQ1dAiL/USwMgD4cQq+IbhSre9H7Os0+x+VaoRO8tWQsRdwvlJhL/HduaZgatXNajgDrVCzcE7gnRXSsjXZVMDqbqwy7vhtvR/DE8sWZmGErnmH2K+moT+izY/S1yXK2yt6TPM8GG2L4pQpmN95rPeF99bXiTZXpS8qi6YE3wx6qo8rKYN8quAH7Pg8YiJPUwS2ezpkpoaRbwG9pKbExTBgKlUoeBTvBuiE0JqsxIDkWsTdRVst2aJH2AM6TOspPdldvE8NiW5QAN0GkxyvYLpnLelhxphKsCbbI1cbz7nA4w1jB/GNnN9FvK+eNDJ7Tl00fqdZmyTYcv830VbLMI+ONu8g57rmydl5IsFWxVEcXNhUwRywBkmwFTfl4mvkMRPNqRlLWXAOQQyDVTczSgpOJdjaiZKhwrLOnHp9S8jyqOpmxhyyRk3dJfIQLCdWKgYDG1nCCsgy9F2Jd8a0I/hQ2iXBu8GwBA/BQB7BVozbG8Eyg15y7zxsYPJGw1i922UJ1uAlmHvQVoz3tvOWZ0v4dBZNcG5LYYrWPZ8Pc6NVCRlJyjmpoXJYA5BKpFmmrBE1MK7nELxVFq2FQZI/96Ac66qYTcE5Oys8SrRKq5J70bLtlnVwilXJRHMpt3jnQZdOnZIgE6Cc3ZSUOOE9TfLEVWr2Xi4A0BBe+N+1S/LfEewJg8mCvRjhs37tPJiKIs+hNTywr8N/bZ/fS3CWMpc42bjAzo4JXumh1csbHTKDtPrI9ThbgYcoS4ZQlWBa1JpbEoyvKQveYzroGJCWsAzYYKtvBeQx6FJuIcNkUYKl4LU3+i74XE06YoObECvAhFDzclWSLNZeJWJZh7Dwtd3mGfuKvcAUBjUvybA1rwqYTJoelrcZpeYz8Jc6quJV21rXUHr4k7Ct0COss3TFvMSouVhro8P0sLK47zD5/dK3Cn4QtLF0fGQG/tHL4RmYbxqxSvF4tjt+KwI5cuVH1H66UW9pk4MeZUnuYN+Z/hbQEu8I5KbkC7z58cB0OSAp5B2isAH13VxJC+4K91cbPabbMHsad0NDQ0NDQ0NDQ0NDw17xDxRpzXmzha10AAAAAElFTkSuQmCC" alt="f(0) = f0" style="width: 60px; height: 20px;" width="60" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; "><span style=""> and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="f(infinity) = 0" style="width: 65px; height: 19px;" width="65" height="19"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; "><span style="">.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 194.342px 7.91667px; transform-origin: 194.342px 7.91667px; unicode-bidi: normal; "><span style="">Write a function to solve this problem—that is, return values of </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">f</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.2333px 7.91667px; transform-origin: 69.2333px 7.91667px; unicode-bidi: normal; "><span style=""> at specified values of </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">η</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; "><span style="">. </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 7.91667px; transform-origin: 40.8333px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Background</span></span></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.133px 7.91667px; transform-origin: 372.133px 7.91667px; unicode-bidi: normal; "><span style="">The physical problem involves diffusion of a quantity from one point where the concentration is maintained at a constant value into a medium in which the concentration is zero far away. The ODE results from transforming the diffusion equation—a partial differential equation in time and a spatial coordinate—with a similarity solution. </span></span></div></div></div>

Solve

Solution Stats

7 Solutions
4 Solvers

Last Solution submitted on Nov 20, 2021

Last 200 Solutions

Problem Comments

Problem Recent Solvers4

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 51322. Solve an ODE: diffusion problem 1

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers4

Suggested Problems

More from this Author136

Problem Tags

Community Treasure Hunt

Problem 51322. Solve an ODE: diffusion problem 1

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers4

Suggested Problems

More from this Author136

Problem Tags

Community Treasure Hunt

Players