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Computer Algebra Report

Solving

Partial Diﬀerential Equations

Using

Maple 2021 and Mathematica 12.2

Nasser M. Abbasi

January 29, 2024 Compiled on January 29, 2024 at 8:40pm

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 Beam PDE
2.4 Burger’s PDE
2.5 Black Scholes PDE
2.6 Korteweg-deVries PDE
2.7 Tricomi PDE
2.8 Keldysh equation
2.9 Euler-Poisson-Darboux equation
2.10 Chaplygin’s equation
2.11 Cauchy Riemann PDE’s
2.12 Hamilton-Jacobi PDE
2.13 Airy PDE
2.14 Nonlinear PDE’s
2.15 more miscellaneous
3 Schrodinger PDE
3.1 1D
3.2 2D
4 Parabolic PDE’s (Diﬀusion)
4.1 Diﬀusion in 1D
4.2 Diﬀusion in 2D
4.3 Diﬀusion in 3D
5 Elliptic PDE’s (Laplace, Poisson, Helmholtz)
5.1 Laplace in 2D
5.2 Laplace in 3D
5.3 Poisson in 2D
5.4 Helmholtz in 2D
5.5 Helmholtz in 3D
6 Hyperbolic PDE’s (Wave)
6.1 Wave PDE in 1D
6.2 Wave PDE in 2D
6.3 Wave PDE in 3D
7 Handbook of ﬁrst order partial diﬀerential equations
7.1 chapter 1
7.2 chapter 2
7.3 chapter 3
7.4 chapter 4
7.5 chapter 5
7.6 chapter 6
7.7 chapter 7
7.8 chapter 8
7.9 chapter 9
8 Handbook of nonlinear partial diﬀerential equations
8.1 chapter 1