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README.md

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[![Coverage Status](https://coveralls.io/repos/JuliaDiffEq/DiffEqApproxFun.jl/badge.svg?branch=master&service=github)](https://coveralls.io/github/JuliaDiffEq/DiffEqApproxFun.jl?branch=master)
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[![codecov.io](http://codecov.io/github/JuliaDiffEq/DiffEqApproxFun.jl/coverage.svg?branch=master)](http://codecov.io/github/JuliaDiffEq/DiffEqApproxFun.jl?branch=master)
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[![DiffEqApproxFun](http://pkg.julialang.org/badges/DiffEqApproxFun_0.5.svg)](http://pkg.julialang.org/?pkg=DiffEqApproxFun)
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[![DiffEqApproxFun](http://pkg.julialang.org/badges/DiffEqApproxFun_0.6.svg)](http://pkg.julialang.org/?pkg=DiffEqApproxFun)
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DiffEqApproxFun.jl is a component package in the DifferentialEquations ecosystem. It holds the components for solving differential equations using spectral methods defined by types from ApproxFun.jl. Users interested in using this functionality should check out [DifferentialEquations.jl](https://github.com/JuliaDiffEq/DifferentialEquations.jl).
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To define such a problem, we first need to define our inital condition as a `Fun` type:
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```julia
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using DiffEqBase, OrdinaryDiffEq, Sundials, ApproxFun, DiffEqApproxFun
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using DiffEqApproxFun
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S=Fourier()
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u0=Fun->cos(cos-0.1))-cos(cos(0-0.1)),S)
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```
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We can now solve this using any solver:
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```julia
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using OrdinaryDiffEq
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sol=solve(prob,Tsit5()) # OrdinaryDiffEq.jl
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using Sundials
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sol=solve(prob,CVODE_BDF()) # Sundials.jl
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using ODEInterfaceDiffEq
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sol=solve(prob,radau()) # ODEInterfaceDiffEq.jl
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```
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