Journal of Automated Reasoning
Elements of Mathematical Analysis in PVS
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
On the Mechanization of Real Analysis in Isabelle/HOL
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Constructive Reals in Coq: Axioms and Categoricity
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
A Decision Procedure for Linear "Big O" Equations
Journal of Automated Reasoning
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Floats and Ropes: A Case Study for Formal Numerical Program Verification
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
On the partial difference equations of mathematical physics
IBM Journal of Research and Development
A constructive formalization of the fundamental theorem of calculus
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
A HOL theory of euclidean space
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
Verification of a heat diffusion simulation written with orléans skeleton library
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
Improving real analysis in coq: a user-friendly approach to integrals and derivatives
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program
Journal of Automated Reasoning
The picard algorithm for ordinary differential equations in coq
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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Popular finite difference numerical schemes for the resolution of the one-dimensional acoustic wave equation are well-known to be convergent. We present a comprehensive formalization of the simplest scheme and formally prove its convergence in Coq. The main difficulties lie in the proper definition of asymptotic behaviors and the implicit way they are handled in the mathematical pen-and-paper proofs. To our knowledge, this is the first time this kind of mathematical proof is machine-checked.