odeSolver.jl

### A Pluto.jl notebook ###
# v0.19.38

using Markdown
using InteractiveUtils

# ╔═╡ ce035857-9ec3-4942-8ff4-bc3f39cc5687
begin
	using DifferentialEquations
	using Plots
	using FastGaussQuadrature
	using DelimitedFiles
	#using Integrals
	using Trapz
	using Bessels
	using HDF5
	using QuadGK
	using Printf
end

# ╔═╡ 588376cc-c654-4782-ad4e-6ea9fcb4491f
begin
N=34
Rd=4.282;
rhat=range(0,Rd,500);
eps=1.0;
k1=16.4706/Rd;
ss=0.004;
a0=eps/k1;
epsn=a0/Rd;
b_d=0.8;b=b_d/Rd;
r=rhat/Rd;
j1 = approx_besselroots(1,N);
t_hat=0:0.001:.485*6;
gg=981;
t0n=t_hat*sqrt(gg/Rd);
dt=0.001*sqrt(gg/Rd);
Boc = 222;
rr = 4;
rri = 0.25;
Bo = rr^2*Boc;
kn = j1[1:N];
ω = sqrt.(kn.*(1 .+ kn.^2*ss));






end

# ╔═╡ afcd3f04-b970-4e6d-9741-22ce37cdbf46
(ω,kn)

# ╔═╡ 60e0b33e-5c32-479c-ba10-ce6975cc9e8f
begin
x0=zeros(2*N,1);
for n=1:N
fun(x)=-epsn*x.*(1-(x/b).^2).*exp(-(x/b).^2).*besselj.(0,kn[n].*x);
den(x)= x.*besselj.(0,kn[n]*x).*besselj.(0,kn[n]*x);
x0[n]=quadgk(fun,0,1,rtol=1e-3)[1]/quadgk(den,0,1,rtol=1e-3)[1];
end
end

# ╔═╡ 30ce9fb5-4c20-4bb4-bde9-276a8d328e4e

function nayfeh!(du, u, p, t)
print("time=%f\n",float(t))
   for n = 1:N
	    sum = 0;
	    Ga=h5read("./hd5_newdir/Ga_$n.h5","mygroup2/Ga")
	    Ch=h5read("./hd5_newdir/Ch_$n.h5","mygroup2/Ch")
	
	
		sum=u[1:N,1]'*Ga[1:N,1:N]*(-(ω .^2).*u[1:N,1])+u[N+1:2*N]'*Ch[1:N,1:N]*u[N+1:2*N];
	
	
	
	    du[n]=u[n+N];
	    du[n+N]=-ω[n]^2*u[n]-sum;
	   
	end
	

end


# ╔═╡ 82c6c87f-461a-4a56-b3cf-ade52a153ec6


# ╔═╡ 469f95b9-583d-420c-a1b2-b6c7f7d5967f
begin
	tspan=(0,t0n[end]);
    prob=ODEProblem(nayfeh!, x0, tspan)
	sol=solve(prob, saveat = dt);
end

# ╔═╡ f981ce70-ad30-4c82-919e-33cd4292e153
writedlm("new_nonlin.dat", sol.u)

# ╔═╡ cca2edd0-685b-47b0-9a42-aeb67a3b6b00
# ╠═╡ disabled = true
#=╠═╡
begin
 etan = zeros(length(Y),1);
p=plot()
 end
  ╠═╡ =#

# ╔═╡ 4ce6083f-68a3-4d59-a811-b58675af884f
# ╠═╡ disabled = true
#=╠═╡
 begin
for t in 1:length(sol.t)
	for ss in 1:length(Y)
		 summ=0;
		for ll in 1:N
			summ = summ+ besselj.(0,kn[ll]*Y[ss])*sol.u[t][ll];
		end
		etan[ss]=summ
	end
	p= plot(Y,etan)
	
end
display(p)
 end
  ╠═╡ =#

# ╔═╡ 2c0df57e-c3bd-4800-939b-540d9080c21c
   

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[[deps.Xorg_xcb_util_renderutil_jll]]
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git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.6+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.39.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.5+0"

[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.9+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.43.0+0"

[[deps.gperf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
version = "3.1.1+0"

[[deps.libaec_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "eddd19a8dea6b139ea97bdc8a0e2667d4b661720"
uuid = "477f73a3-ac25-53e9-8cc3-50b2fa2566f0"
version = "1.0.6+1"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+1"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.11.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.18.0+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "93284c28274d9e75218a416c65ec49d0e0fcdf3d"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.40+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.6+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.52.0+1"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
"""

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