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Adding dt=h for Euler decay solution

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Noah L. Schrick 2023-02-15 14:27:04 -06:00
parent 36865632fa
commit 0eb34e59ac
1 changed files with 6 additions and 3 deletions
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Schrick-Noah_Homework-3.R
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@ -89,15 +89,18 @@ k <- 0.03
y0 <- 100 y0 <- 100
decay.euler.sol <- my_euler(f=function(t,y){decay.f(t,y,k=k)}, decay.euler.sol <- my_euler(f=function(t,y){decay.f(t,y,k=k)},
y0, t0, tfinal, dt=1) y0, t0, tfinal, dt=h)
plot(decay.euler.sol$t,decay.euler.sol$y) plot(decay.euler.sol$t,decay.euler.sol$y, xlab="t", ylab="y",
main="Euler Numerical Solution for the decay ode dy/dt=-ky")
par(new=T) par(new=T)
lines(seq(t0,tfinal,len=50), lines(seq(t0,tfinal,len=50),
y0*exp(-k*seq(t0,tfinal,len=50)), col="red") y0*exp(-k*seq(t0,tfinal,len=50)), col="red")
decay.rk4.sol <- my_rk4(f=function(t,y){decay.f(t,y,k=k)}, decay.rk4.sol <- my_rk4(f=function(t,y){decay.f(t,y,k=k)},
y0, t0, tfinal) y0, t0, tfinal)
plot(decay.rk4.sol$t,decay.rk4.sol$y) plot(decay.rk4.sol$t,decay.rk4.sol$y, xlab="t", ylab="y",
main="RK4 Numerical Solution for the decay ode dy/dt=-ky")
par(new=T) par(new=T)
lines(seq(t0,tfinal,len=50), lines(seq(t0,tfinal,len=50),
y0*exp(-k*seq(t0,tfinal,len=50)), col="red") y0*exp(-k*seq(t0,tfinal,len=50)), col="red")