Gene

Boundary value problem

Applied mathematics

Semi-elliptic operator

Economics

Biochemistry

Dentistry

Differential operator

Poisson's equation

Calculus (dental)

Mathematics

Transcription factor

Mathematical analysis

Repressor

Medicine

Chemistry

Partial differential equation

Finance

Operator (biology)

Order (exchange)

Computer Methods in Applied Mechanics and Engineering

A higher order nonlocal operator method for the solution of boundary value problems is developed. The proposed higher order nonlocal operator brings several advantages as compared to the original nonlocal operator method (Ren et al., 2020) which only ensures first-order convergence. Furthermore, it can be applied to directly and efficiently obtain all partial derivatives of higher orders simultaneously without the need of using shape functions. Only the functionals based on the nonlocal operators (termed as operator functional) are needed to obtain the final discrete system of equations, which significantly facilitates the implementation. Several numerical examples are presented to show the effectiveness and accuracy of the proposed higher order nonlocal operator method including the solution of the Poisson equation in 2–5 dimensional space, Kirchhoff and von Kármán plate problems, incompressible elastic materials as well as phase field modeling of fracture.

A higher order nonlocal operator method for solving partial differential equations