09-23-2026, 07:53 PM
Numerical Partial Differential Equations by James H. Adler, Hans De Sterck, Scott MacLachlan, and Luke Olson is a comprehensive 2025 textbook on the numerical approximation of partial differential equations (PDEs), aimed at advanced undergraduate and graduate students in applied mathematics, scientific computing, science, and engineering. It begins with the mathematical foundations of PDEs and numerical methods, then develops the three major discretization approaches: finite differences, finite elements, and finite volumes. The book emphasizes fundamental concepts such as consistency, stability, accuracy, and convergence, using prototypical elliptic, parabolic, and hyperbolic equations to explain how continuous PDEs are transformed into computational problems.
The later chapters move toward large-scale scientific computing, focusing on the linear systems generated by discretization and the iterative algorithms used to solve them. Topics include Krylov methods, preconditioning, multigrid methods, advanced finite-element and finite-volume discretizations, and systems of conservation laws relevant to applications such as fluid dynamics, electromagnetics, and aerospace simulations.
A major theme is the connection between mathematical properties of a PDE, the quality of its discretization, and the computational cost of obtaining an accurate solution. With 591 pages, the book therefore serves both as an introduction to numerical PDEs and as a bridge toward modern computational mathematics and high-performance scientific computing.
BOOK
The later chapters move toward large-scale scientific computing, focusing on the linear systems generated by discretization and the iterative algorithms used to solve them. Topics include Krylov methods, preconditioning, multigrid methods, advanced finite-element and finite-volume discretizations, and systems of conservation laws relevant to applications such as fluid dynamics, electromagnetics, and aerospace simulations.
A major theme is the connection between mathematical properties of a PDE, the quality of its discretization, and the computational cost of obtaining an accurate solution. With 591 pages, the book therefore serves both as an introduction to numerical PDEs and as a bridge toward modern computational mathematics and high-performance scientific computing.
BOOK
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