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Computer Algebra Report

Solving

Partial Diﬀerential Equations

Using

Maple 2020.2 and Mathematica 12.2

Nasser M. Abbasi

January 29, 2024 Compiled on January 29, 2024 at 10:40pm

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