[{"id":"Q51846190","articles":[{"title":"Butcher tableau","article":"https://en.wikipedia.org/wiki/Butcher_tableau","isPartOf":"https://en.wikipedia.org/"}],"created":"2026-04-08T21:55:31.489Z","description":"table containing the coefficients of Runge-Kutta method","externalLinks":{},"name":{"name":"Butcher tableau","label":"Butcher tableau","prefLabel":"Butcher tableau"},"record_type":"entity","statements":{"P527":[{"id":"Q51846190-f3579899-4d27-1ee6-533e-dc423f304f5e","stmts":[{"p":"P527","o":"Q97664752"}],"quals":[{"p":"P7235","o":"<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>A</mi></mstyle></mrow></math>"}]},{"id":"Q51846190-91912308-4ac5-3296-a970-e66e42b27611","stmts":[{"p":"P527","o":"Q97664754"}],"quals":[{"p":"P7235","o":"<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><msup><mi>𝐛</mi><mrow data-mjx-texclass=\"ORD\"><mi>𝐓</mi></mrow></msup></mrow></mstyle></mrow></math>"}]},{"id":"Q51846190-958eefc7-4b53-37c9-56fa-ed1b7c025e75","stmts":[{"p":"P527","o":"Q97664755"}],"quals":[{"p":"P7235","o":"<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mi>𝐜</mi></mrow></mstyle></mrow></math>"}]}],"P180":[{"id":"Q51846190-f1212367-4361-0874-25aa-8056ca6ac326","stmts":[{"p":"P180","o":"Q725944"}]}],"P138":[{"id":"Q51846190-4d4cdbad-484d-5a79-6ef1-72d3aee9c1eb","stmts":[{"p":"P138","o":"Q607227"}]}],"P2534":[{"id":"Q51846190-7821d5b2-4906-8b4f-b66d-dc3db9bcbd4c","stmts":[{"p":"P2534","o":"<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mtable><mtr><mtd class=\"mwe-math-matrix-bottom mwe-math-matrix-right\"><mrow data-mjx-texclass=\"ORD\"><mi>𝐜</mi></mrow></mtd><mtd class=\"mwe-math-matrix-bottom mwe-math-matrix-left\"><mi>A</mi></mtd></mtr><mtr><mtd class=\"mwe-math-matrix-top mwe-math-matrix-right\"></mtd><mtd class=\"mwe-math-matrix-top mwe-math-matrix-left\"><mrow data-mjx-texclass=\"ORD\"><msup><mi>𝐛</mi><mrow data-mjx-texclass=\"ORD\"><mi>𝐓</mi></mrow></msup></mrow></mtd></mtr></mtable><mo stretchy=\"false\">=</mo><mtable><mtr><mtd class=\"mwe-math-matrix-right\"><msub><mi>c</mi><mrow data-mjx-texclass=\"ORD\"><mn>1</mn></mrow></msub></mtd><mtd class=\"mwe-math-matrix-left\"><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mn>11</mn></mrow></msub></mtd><mtd><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mn>12</mn></mrow></msub></mtd><mtd><mo>&#x2026;</mo></mtd><mtd><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>1</mn><mi>s</mi></mrow></mrow></msub></mtd></mtr><mtr><mtd class=\"mwe-math-matrix-right\"><msub><mi>c</mi><mrow data-mjx-texclass=\"ORD\"><mn>2</mn></mrow></msub></mtd><mtd class=\"mwe-math-matrix-left\"><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mn>21</mn></mrow></msub></mtd><mtd><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mn>22</mn></mrow></msub></mtd><mtd><mo>&#x2026;</mo></mtd><mtd><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>2</mn><mi>s</mi></mrow></mrow></msub></mtd></mtr><mtr><mtd class=\"mwe-math-matrix-right\"><mo stretchy=\"false\">⋮</mo></mtd><mtd class=\"mwe-math-matrix-left\"><mo stretchy=\"false\">⋮</mo></mtd><mtd><mo stretchy=\"false\">⋮</mo></mtd><mtd><mo stretchy=\"false\">⋱</mo></mtd><mtd><mo stretchy=\"false\">⋮</mo></mtd></mtr><mtr><mtd class=\"mwe-math-matrix-bottom mwe-math-matrix-right\"><msub><mi>c</mi><mrow data-mjx-texclass=\"ORD\"><mi>s</mi></mrow></msub></mtd><mtd class=\"mwe-math-matrix-bottom mwe-math-matrix-left\"><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>s</mi><mn>1</mn></mrow></mrow></msub></mtd><mtd class=\"mwe-math-matrix-bottom\"><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>s</mi><mn>2</mn></mrow></mrow></msub></mtd><mtd class=\"mwe-math-matrix-bottom\"><mo>&#x2026;</mo></mtd><mtd class=\"mwe-math-matrix-bottom\"><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>s</mi><mi>s</mi></mrow></mrow></msub></mtd></mtr><mtr><mtd class=\"mwe-math-matrix-top mwe-math-matrix-right\"></mtd><mtd class=\"mwe-math-matrix-top mwe-math-matrix-left\"><msub><mi>b</mi><mrow data-mjx-texclass=\"ORD\"><mn>1</mn></mrow></msub></mtd><mtd class=\"mwe-math-matrix-top\"><msub><mi>b</mi><mrow data-mjx-texclass=\"ORD\"><mn>2</mn></mrow></msub></mtd><mtd class=\"mwe-math-matrix-top\"><mo>&#x2026;</mo></mtd><mtd class=\"mwe-math-matrix-top\"><msub><mi>b</mi><mrow data-mjx-texclass=\"ORD\"><mi>s</mi></mrow></msub></mtd></mtr><mtr><mtd class=\"mwe-math-matrix-right\"></mtd><mtd class=\"mwe-math-matrix-left\"><msubsup><mi>b</mi><mrow data-mjx-texclass=\"ORD\"><mn>1</mn></mrow><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">*</mo></mrow></msubsup></mtd><mtd><msubsup><mi>b</mi><mrow data-mjx-texclass=\"ORD\"><mn>2</mn></mrow><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">*</mo></mrow></msubsup></mtd><mtd><mo>&#x2026;</mo></mtd><mtd><msubsup><mi>b</mi><mrow data-mjx-texclass=\"ORD\"><mi>s</mi></mrow><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">*</mo></mrow></msubsup></mtd></mtr></mtable></mstyle></mrow></math>"}]}],"P1687":[{"id":"Q51846190-5f689422-4901-63a1-828b-7ddb9a365cea","stmts":[{"p":"P1687","o":"P8558"}]}],"P279":[{"id":"Q51846190-1335D0BF-6465-402B-9D76-559A7717F0C9","stmts":[{"p":"P279","o":"Q496946"}]}],"P6104":[{"id":"Q51846190-1A65BE16-BA40-456D-95B2-3F4D57E7EEAB","stmts":[{"p":"P6104","o":"Q8487137"}]}]},"values":{}}]