II.
LibraryProcess overview
Reference · livelib-process:mathematics--pde-solver-selection
pde-solver-selection overview
Guide selection of appropriate numerical methods for partial differential equations based on problem characteristics (elliptic, parabolic, hyperbolic), boundary conditions, and accuracy requirements.
Attributes
displayName
pde-solver-selection
description
Guide selection of appropriate numerical methods for partial differential equations
based on problem characteristics (elliptic, parabolic, hyperbolic), boundary conditions, and accuracy requirements.
libraryPath
library/specializations/domains/science/mathematics/pde-solver-selection.js
specialization
mathematics
references
- - LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations - Morton & Mayers, Numerical Solution of PDEs - Hughes, The Finite Element Method - Trefethen, Spectral Methods in MATLAB
example
const result = await orchestrate('specializations/domains/science/mathematics/pde-solver-selection', {
pdeDescription: 'Heat diffusion in 2D rectangular domain',
pdeEquation: 'u_t = alpha * (u_xx + u_yy)',
boundaryConditions: { type: 'Dirichlet', values: 'fixed temperature on all boundaries' },
domain: { shape: 'rectangle', dimensions: [1, 1] },
accuracyRequirements: { spatialOrder: 2, temporalOrder: 2, relativeTolerance: 1e-6 }
});
usesAgents
- pde-expert
- numerical-analyst
Outgoing edges
lib_applies_to_domain1
- domain:mathematics·DomainMathematics
lib_belongs_to_specialization2
- specialization:computational-mathematics·SpecializationComputational Mathematics
- specialization:mathematics·SpecializationMathematics
lib_implements_workflow1
- workflow:experiment-design·WorkflowExperiment Design
lib_involves_role2
- role:research-engineer·RoleResearch Engineer
- role:computational-scientist·RoleComputational Scientist
lib_requires_skill_area3
- skill-area:statistical-analysis·SkillAreaStatistical Analysis
- skill-area:mathematical-reasoning·SkillAreaMathematical Reasoning
- skill-area:data-analysis·SkillAreaData Analysis
uses_agent2
- lib-agent:mathematics--pde-expert·LibraryAgentpde-expert
- lib-agent:mathematics--numerical-analyst·LibraryAgentnumerical-analyst
Incoming edges
None.