Peridynamics for Numerical Inversion of Laplace Transforms Using Post's Formula

Numerical inversion of the Laplace transform remains a challenging problem due to the need to select method‐specific parameters. This study introduces a peridynamics‐enabled Post inversion formula tailored for real‐valued functions with smooth decay. The proposed approach employs the Peridynamic Differential Operator (PDDO) together with Peridynamic Least Squares Minimization (PDLSM) to accurately evaluate high‐order derivatives in the Laplace domain. Numerical results first validate the method using test functions with known analytical inverses and subsequently demonstrate its applicability to solving differential and integral equations. The results indicate that the proposed approach yields accurate and stable time‐domain solutions. This approach does not require prior knowledge of singularities, contour placement, or function‐specific scaling.