Heun's method
The numerical procedure for solving ordinary differential equations with a given initial value created by Karl Heun.
| rdfs:label |
"Heun's method"@en
|
|
skos:alt |
"explicit trapezoid rule"@en
"improved Euler's method"@en
"modified Euler's method"@en
|
| schema:description |
"The numerical procedure for solving ordinary differential equations with a given initial value created by Karl Heun."@en
|
|
schema:date |
"2026-07-29T18:13:28+00:00"^^xsd:dateTime |
| schema:version | 2524431317 |
| wikibase:identifiers | 2 |
| wikibase:sitelinks | 9 |
| wikibase:statements | 12 |
| p:P138 | wd:statement/Q1531998-f13cae2c-4906-b33c-78c2-4f7c22a5bf43 |
| p:P1552 | wd:statement/Q1531998-59c3c7c7-4086-5dd5-5db0-1251139d3cc0 |
| wd:statement/Q1531998-8410d8e7-4582-ed78-9572-98e6c62d1624 | |
| p:P1889 | wd:statement/Q1531998-d1baa28c-4649-087f-26dc-d6e1286de261 |
| p:P2534 | wd:statement/Q1531998-14428eeb-4b2e-e7b2-f1ec-df14d01767f9 |
| p:P31 | wd:statement/Q1531998-6e92fc66-48a9-ae82-187f-b3641c7b7e7f |
| p:P373 | wd:statement/Q1531998-C4609103-CF27-48F3-BE48-48000D587D5D |
| p:P527 | wd:statement/Q1531998-d1ad2282-46b0-b530-9927-30d77603f7bc |
| p:P6104 | wd:statement/Q1531998-57B5D490-66E7-477F-90B0-7CA896FA8215 |
| p:P6366 | wd:statement/Q1531998-B89E4BB2-E9E0-481B-8CD9-31F72FACE933 |
| p:P646 | wd:statement/Q1531998-57D5E41F-8BD1-4D6E-8A40-D0FB7941BFEF |
| p:P8558 | wd:statement/Q1531998-f9f3e539-4716-7215-420e-151fece333e7 |
|
p:direct- |
<https:/ |
| wdt:P138 | Karl Heun |
| wdt:P1552 | number of stages |
| order of convergence | |
| wdt:P1889 | trapezoidal rule |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>y</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow></msub></mtd><mtd><mo stretchy="false">=</mo><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">+</mo><mi>h</mi><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow></msub></mtd><mtd><mo stretchy="false">=</mo><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>h</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">+</mo><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow></msub><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>y</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P31 | explicit Runge–Kutta method |
| wdt:P373 | "Heun's method" |
| wdt:P527 | Euler method |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "136491612" |
| wdt:P646 | "/m/02rr57j" |
| wdt:P8558 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable columnspacing="1em" rowspacing="4pt" columnalign="center center center "><mtr><mtd class="mwe-math-matrix-right"><mn>0</mn></mtd><mtd class="mwe-math-matrix-left"><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-matrix-bottom mwe-math-matrix-right"><mn>1</mn></mtd><mtd class="mwe-math-matrix-bottom mwe-math-matrix-left"><mn>1</mn></mtd><mtd class="mwe-math-matrix-bottom"><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-matrix-top mwe-math-matrix-right"></mtd><mtd class="mwe-math-matrix-top mwe-math-matrix-left"><mn>1</mn><mo lspace="0" rspace="0">/</mo><mn>2</mn></mtd><mtd class="mwe-math-matrix-top"><mn>1</mn><mo lspace="0" rspace="0">/</mo><mn>2</mn></mtd></mtr><mtr><mtd class="mwe-math-matrix-right"></mtd></mtr></mtable></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
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