Problem 51625. Solve an ODE: diffusion problem 2

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 statement</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(f+eta f') = 0\"/></w:customXmlPr><w:r><w:t>f\\prime\\prime+a(f+\\eta f\\prime)=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>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 function </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\"/></w:customXmlPr><w:r><w:t>f</w:t></w:r></w:customXml><w:r><w:t> and its derivatives vanish at infinity, and it is subject to the constraint</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=\"integral(f,{eta,-inf,inf}) = 1\"/></w:customXmlPr><w:r><w:t>\\int_{-\\infty}^\\infty fd\\eta=1</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>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:attr w:name=\"altTextString\" w:val=\"f\"/></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 instantaneously injected at a point—for example, a spill of a contaminant in an initially clean river. 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: 317px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 158.5px; transform-origin: 407px 158.5px; 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: 63.0083px 7.91667px; transform-origin: 63.0083px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Problem statement</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(f+eta f') = 0" style="width: 130px; height: 19px;" width="130" 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: 42px; 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 21px; text-align: left; transform-origin: 384px 21px; 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: 44.3333px 7.91667px; transform-origin: 44.3333px 7.91667px; unicode-bidi: normal; "><span style="">. The function </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: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; "><span style=""> and its derivatives vanish at infinity, and it is subject to the constraint</span></span></div><div style="block-size: 44px; 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 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img src="data:image/png;base64,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" alt="integral(f,{eta,-inf,inf}) = 1" style="width: 78px; height: 44px;" width="78" height="44"></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: 349.967px 7.91667px; transform-origin: 349.967px 7.91667px; unicode-bidi: normal; "><span style="">The physical problem involves diffusion of a quantity instantaneously injected at a point—for example, a spill of a contaminant in an initially clean river. 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

5 Solutions
4 Solvers

Last Solution submitted on Jan 24, 2022

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 51625. Solve an ODE: diffusion problem 2

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers4

Suggested Problems

More from this Author164

Problem Tags

Community Treasure Hunt

Problem 51625. Solve an ODE: diffusion problem 2

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers4

Suggested Problems

More from this Author164

Problem Tags

Community Treasure Hunt

Players