SIAM Journal on Scientific Computing· 2026Q1
A Parallel-in-Time Newton’s Method-Based ODE Solver
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- Q1SCImago
- 2026year
Short summary
A novel parallel-in-time ODE solver using Newton's method achieves logarithmic span complexity via parallel prefix sums, outperforming the Parareal method.
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Key points
- Introduces a novel parallel-in-time solver for nonlinear ODEs.
- Reformulates ODE solution as a root-finding problem solved by Newton's method.
- Parallelizes Newton's method steps using parallel prefix sums (parallel scan).
- Achieves logarithmic span complexity.
- Demonstrates improved runtime performance over the Parareal method via simulations.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract. In this article, we introduce a novel parallel-in-time solver for nonlinear ordinary differential equations (ODEs). We state the numerical solution of an ODE as a root-finding problem that we solve using Newton’s method. The affine recursive operations arising in Newton’s step are parallelized in time by using parallel prefix sums, that is, parallel scan operations, which leads to a logarithmic span complexity. This yields an improved runtime compared to the previously proposed Parareal method. We demonstrate the computational advantage through numerical simulations of various systems of ODEs.
The authors' abstract, as published at the source. SIAM Journal on Scientific Computing, 2026 · DOI ↗
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Field: Hardware and Architecture
Hardware and ArchitectureComputer Science