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annotate +time/+rk/rungekuttaDiscreteData.m @ 933:34b3d092a4d0 feature/timesteppers

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Add methods timePoints and quadWeights to Rungekutta class.
author Martin Almquist <malmquist@stanford.edu>
date Mon, 03 Dec 2018 16:49:43 -0800
parents 34d882bffae4
children
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34d882bffae4 Add stepping function for RK with discrete data.
Martin Almquist <malmquist@stanford.edu>
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1 % Takes one time step of size dt using the rungekutta method
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Martin Almquist <malmquist@stanford.edu>
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2 % starting from @arg v.
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3 %
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Martin Almquist <malmquist@stanford.edu>
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4 % discreteData contains (a part of) the forcing function, already
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5 % evaluated on the space-time grid.
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6 %
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7 % ODE: dv/dt = F(v,t) + discreteData(:, nt), where nt denotes the current time-point.
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8 %
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Martin Almquist <malmquist@stanford.edu>
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9 % coeffs is a struct holding the RK coefficients
34d882bffae4 Add stepping function for RK with discrete data.
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10 % for the specific method.
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11 % Also returns the stage approximations (V) and stage rates (K).
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12 function [v, V, K] = rungekuttaDiscreteData(v, t , dt, F, coeffs, discreteData, n)
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13 % Compute the intermediate stages k
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14 K = zeros(length(v), coeffs.s);
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15 V = zeros(length(v), coeffs.s);
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16 for i = 1:coeffs.s
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17 u = v;
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18 for j = 1:i-1
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19 u = u + dt*coeffs.a(i,j)*K(:,j);
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20 end
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21 V(:,i) = u;
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22 K(:,i) = F(u,t+coeffs.c(i)*dt);
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23 K(:,i) = K(:,i) + discreteData(:, n*coeffs.s + i);
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24 end
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25 % Compute the updated solution as a linear combination
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26 % of the intermediate stages.
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27 for i = 1:coeffs.s
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28 v = v + dt*coeffs.b(i)*k(:,i);
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29 end
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30 end