This is the homepage of Joshua Ira Shapiro.


Welcome. I dig math and music.

I am a Master's student in the Applied Mathematics program at Stony Brook University.


AMS 528 Homework 5


Laplacian Solved Using Jacobi Iteration


Laplacian Solved Using Gauss-Seidel Iteration


Laplacian Solved Using SOR Iteration



AMS 528 Homework 4


Problem 2


Godunov Scheme 200 w/ Godunov 3200 as Exact Solution


Lax-Friedrich Scheme 200 w/ Godunov 3200 as Exact Solution


Lax-Wendroff Scheme 200 w/ Godunov 3200 as Exact Solution


Problem 3

Godunov Scheme w/ Roe Approximation


Godunov Scheme w/ Enquist-Osher Approximation


Godunov Scheme w/ van Leer Approximation



Problem 4



Superbee Limiter


van Leer Limiter


C-O Limiter



Beam-Warming Limiter



Problem 5


Superbee Limiter w/ different initial conditions


van Leer Limiter w/ different initial conditions


C-O Limiter w/ different initial conditions



Beam-Warming Limiter w/ different initial conditions



AMS 528 Homework 2 & 3


Upwind Decomposed Wave


Lax-Wendroff Decomposed Wave


Crank-Nicolson CFL=.8, N =200


Crank-Nicolson CFL=.8, N =400


Crank-Nicolson CFL=.8, N =800


Crank-Nicolson CFL=.8, N 1600


Crank-Nicolson CFL=1.5, N =200


Crank-Nicolson CFL=1.5, N =400


Crank-Nicolson CFL=1.5, N =800


Crank-Nicolson CFL=1.5, N =1600



Central-Implicit CFL=.8, N =200


Central-Implicit CFL=.8, N =400


Central-Implicit CFL=.8, N =800


Central-Implicit CFL=.8, N =1600



Central-Implicit CFL=1.5, N =200


Central-Implicit CFL=1.5, N =400


Central-Implicit CFL=1.5, N =800


Central-Implicit CFL=1.5, N =1600



Upwind V1


Upwind V2


Upwind V3


Lax Wendroff V1


Lax Wendroff V2


Lax Wendroff V3


AMS 528 Homework 1

Problem 2

Lax-Friedrich scheme


Lax-Wendroff scheme


MacCormack scheme


Upwind scheme


Leapfrog scheme


Problem 5


Downwind scheme


Central difference scheme


Lax-Friedrich scheme revisited




Comic from xkcd:




In my free time I like to
     yoga out     


         jam on my djembe



   go to concerts!          







Here are a few paintings I like:
Plain Near Auvers
Vincent Van Gogh

Forgotten Horizon
Salvador Dali



Cool websites:
Xkcd
Spiked Math