annotate +time/+cdiff/cdiff.m @ 888:8732d6bd9890
feature/timesteppers
Add general Runge-Kutta class
- Add a general Runge-Kutta class which time integrates the solution based on coefficients obtained from a Butcher tableau
- Add butcher tableau which returns coefficents for the specified Runge-Kutta method
- Remove RungKutta4proper, since obsolete
| author |
Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
| date |
Thu, 15 Nov 2018 17:10:01 -0800 |
| parents |
48b6fb693025 |
| children |
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| rev |
line source |
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1 % Takes a step of
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2 % v_tt = Dv+Ev_t+S
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3 %
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4 % 1/k^2 * (v_next - 2v + v_prev) = Dv + E 1/(2k)(v_next - v_prev) + S
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5 %
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6 function [v_next, v] = cdiff(v, v_prev, k, D, E, S)
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7 % 1/k^2 * (v_next - 2v + v_prev) = Dv + E 1/(2k)(v_next - v_prev) + S
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8 % ekv to
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9 % A v_next = B v + C v_prev + S
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10 I = speye(size(D));
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11 A = 1/k^2 * I - 1/(2*k)*E;
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12 B = 2/k^2 * I + D;
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13 C = -1/k^2 * I - 1/(2*k)*E;
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14
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15 v_next = A\(B*v + C*v_prev + S);
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16 end |
