Code covered by the BSD License

Highlights from
Chebpack

A=fact(a,m)
B=Ex4_delay_main use: B=Ex4_delay_main;
D=deriv(n,dom) D: the spectral differentiation matrix D (sparse)
Ex1( n)
Ex1_delay( n , alpha , K )
Ex1_delay_cta( n , alpha, K )
Ex2( n) Example 2
Ex3( n)
Ex3_delay( n,K )
Ex4( n) Example 4
Ex4_delay( n , lambda , K )
Ex5( n) Example 5
Ex6_delay( n , p , alpha , be... Mackey-Glass equation
Ex6_delay_dde(p , alpha , bet...
S=dev(n,x,dom,lx)
T=cpv(n,xc,dom)
X=mult(n,dom)
[J,J0]=prim(n,dom) J: the matrix of the spectral primitive (sparse)
[LL,evec, x]=Greenberg6(n,dom... From: Leon Greenberg, Marco Marletta, Algorithm 775: the code SLEUTH for
[S1,S]=monomials(p) Scaling matrix S
[c,cor,kod]=lisc(Nfun,lam,phi... % Lyapunov-Schmidt reduction
[c,rez,drez,kod]=as(Nfun,lam,... % Calculates the coefficients c of the function associated to c0
[e]=mlf(alf,bet,c,fi);
[int,grid]=quad_ex2(n,a,x,tol...
[lam,phi,x,tau]=eig42E(n,dom,...
[lam,phi,x]=KdV_eig(n,dom,kin... From: W. Heinrichs, Spectral Approximation of third order problems,
[lam,phi,x]=OrrSom(n,dom,kind...
[lam,phi,x]=eig42D(n,dom,kind... From D. Gottlieb, S. A. Orszag, Numerical Anlaysis of Spectral Methods:
[lam,phi,x]=eig_ode2(n,dom,ki... solves the eigenvalue problems for second order ode
[lam,phi,x]=eig_ode2_ex1(n,do...
[lam,phi,x]=eig_ode2_ex2(n,do...
[lam,phi,x]=eig_ode2_ex3(n,do...
[lam,phi,x]=eig_ode2_test(n,d...
[lam,phi,x]=eig_ode3_test(n,d...
[lam,phi,x]=eig_ode4_2_test(n...
[lam,phi,x]=eig_ode4_test(n,d...
[lamv,phiv,lamu,phiu,x]=Lutze... From: J. LUTZEN, Sturm and Liouville's Work on Ordinary
[t,err]=quad_ex1
[t,solnum2]=Ex6pant(n) Example 6
[t,solnum]=Ex5pant(n) Example 5
[t,y]=ex2(n) From C. Marriott and C. DeLisle, Effects of discontinuities in the
[t1opt,I1opt,F]=ex3
[time,x,y]=ex6(k,v0x,v0y) Shampine's Example ch2ex3.m from
[x,DF,T,DFphys]=deriv_frac(n,... DF: the matrix of the fractional Caputo derivative
[x,solnum,A,b]=pde_lin_ex1(n,...
[x,solnum]=deriv_frac_ex1(n,d...
[x,solnum]=deriv_frac_ex2(n,d...
[x,solnum]=deriv_frac_ex2_phy...
[x,solnum]=deriv_frac_ex3(n,d...
[x,solnum]=deriv_frac_ex4(n,d...
[x,solnum]=fred_eq(n,dom,kind... Solves Fredholm integral equations
[x,solnum]=fred_eq_ex1(n,dom,...
[x,solnum]=fred_eq_ex2(n,dom,...
[x,solnum]=fred_eq_ex3(n,dom,...
[x,solnum]=fred_eq_ex4(n,dom,...
[x,solnum]=fred_eq_ex5(n,dom,...
[x,solnum]=ibvp_int_succappro... solves nonlinear Volterra integral equations of the type
[x,solnum]=ibvp_int_succappro...
[x,solnum]=ibvp_ode(n,dom,kin... solves the initial/boundary value problems for a general linear ode using
[x,solnum]=ibvp_ode_ex(n,dom,...
[x,solnum]=ibvp_ode_ex1(n,dom...
[x,solnum]=ibvp_ode_ex2(n,dom...
[x,solnum]=ibvp_ode_ex3(n,dom...
[x,solnum]=ibvp_ode_ex4(n,dom...
[x,solnum]=ibvp_ode_ex8(n,dom...
[x,solnum]=ibvp_ode_int(n,dom... solves the initial/boundary value problems for a general linear ode using
[x,solnum]=ibvp_ode_int_ex(n,...
[x,solnum]=ibvp_ode_int_ex1(n...
[x,solnum]=ibvp_ode_int_ex2(n...
[x,solnum]=ibvp_ode_int_ex3(n...
[x,solnum]=ibvp_ode_int_test(...
[x,solnum]=ibvp_ode_newton(n,... solves the initial/boundary value problems for second order differential
[x,solnum]=ibvp_ode_newton_ex...
[x,solnum]=ibvp_ode_newton_ex...
[x,solnum]=ibvp_ode_newton_te...
[x,solnum]=ibvp_ode_succappro... solves nonlinear initial/boundary value problems for a general ode
[x,solnum]=ibvp_ode_succappro...
[x,solnum]=ibvp_ode_succappro...
[x,solnum]=ibvp_ode_test(n,do...
[x,solnum]=ibvp_sys(n,dom,kin... solves initial value problems for first order systems
[x,solnum]=ibvp_sys_ex2(n,dom...
[x,solnum]=ibvp_sys_ex3(n,dom...
[x,solnum]=ibvp_sys_ex3_int(n...
[x,solnum]=ibvp_sys_newton_ex...
[x,solnum]=ibvp_sys_test(n,do...
[x,solnum]=pde_lin_matr_ex1(n...
[x,solnum]=pde_lin_matr_test(...
[x,solnum]=volt_eq(n,dom,kind... Solves Volterra integral equations
[x,solnum]=volt_eq_creep(n,do... Solves Volterra integral equations
[x,t,solnum,I1,I2,I3,time]=Kd...
[x,t,solnum]=pde_lin(n,dom, k... Solves linear evolution partial differential problems
[x,t,solnum]=pde_lin_matr(n,d... Solves linear partial differential problems of evolution type
[x,t,solnum]=pde_lin_test(n,d...
[x,t,solnum]=pde_nonlin(n,dom... Solves nonlinear evolution partial differential problems
[x,t,solnum]=pde_nonlin_ex1(n...
[x,t,solnum]=pde_nonlin_ex2(n...
[x,t,solnum]=pde_nonlin_ex4(n...
[x,t,solnum]=pde_nonlin_test(...
[xg,solnumg]=ibvp_sys_newton_...
[xg,solnumg]=ibvp_sys_newton_...
[xg,solnumg]=ibvp_sys_succapp... solves nonlinear initial value problems for first order systems
[xg,solnumg]=ibvp_sys_succapp...
[xg,solnumg]=ibvp_sys_succapp...
[xm,yvm]=test3(n,dom,kind,p,e... p: order of the equation, ep: the continuation parameter
[xx,solnum]=ibvp_ode_split(n,... solves the initial/boundary value problems for a general linear ode using
[xx,solnum]=ibvp_ode_split_ex...
[xx,solnum]=ibvp_ode_split_ex...
[xx,solnum]=ibvp_ode_split_ex...
[xx,solnum]=ibvp_ode_split_te...
[z,fz,m]=chebroots(c,dom,loc,... Calculates the roots of f
e=OrrSomDMS(N,R) The script file OrrSomDMS.m computes the eigenvalues of the Orr-Sommerfeld
e=eig42DMS(N)
fact_ex1(N,dom,kind) Calculates cosh(X) using fact and funm from Matlab
quad_ex3
quadcheb(myfun,n,dom,kind,tol... Calculates the integral of "myfun" on "dom" using n Chebyshev
sol=Ex1_delay_dde(alpha,K)
sol=Ex3_delay_dde use sol=Ex3_delay_dde;
test1
test2
wip( f,g,r,wleg) f,g,r values on Legendre grid
Boussinesq.m
ElDaou.m
Ex1pant.m
Ex2_delay.m
Ex2pant.m
Ex3pant.m
Ex4_delay_fig.m
Ex4n0pant.m
Ex4n1pant.m
Ex5_delay.m
KS_evol.m
KS_ode.m
KdV_eig_CHEBFUN.m
OrrSomCHEBFUN.m
barycheb.m
demo_ex6dde.m
deriv_frac_ex5.m
eig42CHEBFUN.m
eig42F.m
ex1.m
ex4.m
ex5.m
ex5_work.m
fred_eq_test.m
ibvp_int_newton_ex1.m
ibvp_int_succapprox_test.m
ibvp_ode_int_ex4.m
ibvp_ode_newton_ex3.m
ibvp_ode_succapprox_ex1.m
ibvp_sys_ex2x2.m
magnitude.m
pd.m
pde_nonlin_ex3.m
rang.m
t2x.m
volt_eq_ex1.m
volt_eq_ex2.m
volt_eq_test.m
x2t.m
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Chebpack

by Damian Trif

15 Jul 2011 (Updated 10 Jun 2013)

The MATLAB package Chebpack solves specific problems for differential or integral equations.

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File Information
Description	The MATLAB package Chebpack solves specific problems for differential or integral equations. It is organized in four modules, corresponding to four levels of complexity. Each level has an associated set of particular examples. The package is based on the Chebyshev tau spectral method applied in operatorial form. Basic documentation is: Damian Trif (2011). Matrix Based Operatorial Approach to Differential and Integral Problems, MATLAB - A Ubiquitous Tool for the Practical Engineer, Clara M. Ionescu (Ed.), ISBN: 978-953-307-907-3, InTech, Available from: http://www.intechopen.com/articles/show/title/matrix-based-operatorial-approach-to-differential-and-integral-problems
Acknowledgements	Chebfun inspired this file.
Required Products	Optimization Toolbox MATLAB
MATLAB release	MATLAB 7.11 (R2010b)

Tags for This File
Everyone's Tags	delay differential equations, differential equations, fractional differential equations, impulsive differential equations, integral equations, mathematics, partial differential equations
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Updates
13 Oct 2011	Change the basic documentation
15 Feb 2012	New examples for multiple positive solutions
30 Mar 2012	New examples for pantograph equation and for Volterra equation
26 Apr 2013	New examples for delay and impulsive differential equations
10 Jun 2013	Corrected some bugs and added new examples with higher order differential problems.

Highlights from Chebpack

Chebpack

Highlights from
Chebpack