Base GRM Rebuild Numerical Methods in Scientific Computing
Numerical Methods in Scientific Computing — Base GRM Rebuild: ToC PART I — SOURCE BEFORE REPRESENTATION 1. What Numerical Computation Is Actually Reconstructing 1.1 Physical source ≠ mathematical representation 1.2 SOURCE ≠ PDE ≠ DISCRETIZATION ≠ MATRIX ≠ SOLUTION_VECTOR 1.3 Observable, state, carrier, law and readout 1.4 Source-owned distinctions and admissible transformations 1.5 Local relation versus global consequence 1.6 What counts as a computational target 1.7 Representation debt and why equations are downstream 1.8 Numerical computation as causal reconstruction 1.9 GRM pipeline: SOURCE→BODY→CARRIER→TRANSPORT→RESIDUE→REPAIR→LIFTBACK 1.10 Failure taxonomy: source failure, model failure, carrier failure, execution failure 1.11 Validation versus internal numerical agreement 2. Source Laws: Balance, Flux, Production and Closure 2.1 Extensive quantity and local density 2.2 Boundary transfer as a source-owned relation 2.3 Internal production and destruction 2.4 Control-vol...