On the analysis of a kind of nonlinear Sobolev equation through locally applied pseudo‐spectral meshfree radial point interpolation
S. Abbasbandy, Elyas Shivanian, Khalid Hammood AL‐Jizani
Abstract
Abstract In this study, we develop an approximate formulation for two‐dimensional nonlinear Sobolev problems by focusing on pseudospectral meshless radial point interpolation (PSMRPI) which is a kind of locally applied radial basis function interpolation and truthfully a meshless approach. In the PSMRPI method, the nodal points do not need to be regularly distributed and can even be quite arbitrary. It is easy to have high order derivatives of unknowns in terms of the values at nodal points by constructing operational matrices. The convergence and stability of the technique in some sense are studied via some examples to show the validity and trustworthiness of the PSMRPI technique.
Topics & Concepts
MathematicsInterpolation (computer graphics)Sobolev spaceRadial basis functionMeshfree methodsNonlinear systemMathematical analysisConvergence (economics)Applied mathematicsPoint (geometry)Finite element methodGeometryComputer scienceComputer graphics (images)Quantum mechanicsPhysicsThermodynamicsEconomic growthEconomicsMachine learningArtificial neural networkAnimationNumerical methods in engineeringNonlinear Waves and SolitonsElectromagnetic Simulation and Numerical Methods