DeSolver

Documentation

Load the package by

using DeSolver

This package solves the givenode model with the initial condition and the time span

odesolve

With the ode model given in the form of

function ode(u, t)
    du = f(u,t)
    ...
return du 

you can solve the ode using

sol = odesolve(ode, ic, tspan,  stepsize=1e-5; method="RK4")

sol.u will give you the numerical solution to the ode

methods

RK4 = Runge Kutta Method of order 4

RK2 = Runge Kutta Method of order 2

Examples

ODEs

Simple first order ODE

function test(u,t)
    du=sin(t)^2*u
    return du
end

sol=odesolve(test, 1., (0.,10.), 1, method="RK4")
plot(map(x->x[1],sol.t),map(x->x[1],sol.u)

Simple second order ODE

function trig(u,t)
    du= u[2]
    ddu = -u[1]
    return [du, ddu]
end

sol=odesolve(trig, [1., 0.], (0.,10.), 1, method="RK4")
plot(map(x->x[1],sol.t),map(x->x[1],sol.u)

PDE

# Number of collocation points 
N = 50
h= pi/N

# create function
function f(u,t)
    du = zeros(length(u))
    for i in 1:length(u)
        if i ==1
            du[1] = (-2u[1] + 2u[2])/h^2
        elseif i == length(u)
            du[length(u)] = (2u[length(u)-1] - 2u[length(u)])/h^2
        else
            du[i] = (u[i-1] - 2u[i] + u[i+1])/h^2
        end
    end
    return du
end

xs=range(0, stop=pi, length=N)
u0=sin.(xs)

sol=odesolve(f, u0, (0.,10.), .1, method="RK4")
 surface(1:10,1:100,(x,y)-> sol.u[y][x], xlabel="x",ylabel="t")

10 Collocation Points, and 10 Timesteps

10 Collocation Points, and 1000 Timesteps

20 Collocation Points, and 100 Timesteps

50 Collocation Points, and 10000 Timesteps