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Computer Algebra Report

Solving

Partial Differential Equations

Using

Maple 2019 and Mathematica 12

Nasser M. Abbasi

January 20, 2020   Compiled on January 20, 2020 at 3:12pm

1 Introduction, Summary of results and lookup table
 1.1 Introduction
 1.2 Results
 1.3 Result lookup table split over number of web page pages
 1.4 Result lookup table on one web page
2 Miscellaneous PDE’s
 2.1 General first order
 2.2 Solved by factoring into two transport equations
 2.3 Schrodinger PDE
 2.4 Beam PDE
 2.5 Burger’s PDE
 2.6 Black Scholes PDE
 2.7 Korteweg-deVries PDE
 2.8 Tricomi PDE
 2.9 Keldysh equation
 2.10 Euler-Poisson-Darboux equation
 2.11 Chaplygin’s equation
 2.12 Cauchy Riemann PDE’s
 2.13 Hamilton-Jacobi PDE
 2.14 Airy PDE
 2.15 Nonlinear PDE’s
 2.16 more miscellaneous
3 Parabolic PDE’s (Diffusion)
 3.1 Diffusion in 1D
 3.2 Diffusion in 2D
 3.3 Diffusion in 3D
4 Elliptic PDE’s (Laplace, Poisson, Helmholtz)
 4.1 Laplace in 2D
 4.2 Laplace in 3D
 4.3 Poisson in 2D
 4.4 Helmholtz in 2D
 4.5 Helmholtz in 3D
5 Hyperbolic PDE’s (Wave)
 5.1 Wave PDE in 1D
 5.2 Wave PDE in 2D
 5.3 Wave PDE in 3D
6 Handbook of first order partial differential equations
 6.1 chapter 1
 6.2 chapter 2
 6.3 chapter 3
 6.4 chapter 4
 6.5 chapter 5
 6.6 chapter 6
 6.7 chapter 7
 6.8 chapter 8
 6.9 chapter 9
7 Handbook of nonlinear partial differential equations
 7.1 chapter 1