Applying the Adomian Method to Solve the Fokker–Planck Equation: A Case Study in Astrophysics - Melina Silva de Lima; José Vicente Cardoso Santos; José Humberto de Souza Prates; Celso Barreto Silva; Davidson Moreira; Marcelo A. Moret (AppliedMath)
The objective of this study is to model astrophysical systems using the nonlinear Fokker–Planck equation, with the Adomian method chosen for its iterative and precise solutions in this context, applying boundary conditions relevant to data from the Rossi X-ray Timing Explorer (RXTE). The results include analysis of 156 X-ray intensity distributions from X-ray binaries (XRBs), exhibiting long-tail profiles consistent with Tsallis q-Gaussian distributions. The corresponding q-values align with the principles of Tsallis thermostatistics. Various diffusion hypotheses—classical, linear, nonlinear, and anomalous—are examined, with q-values further supporting Tsallis thermostatistics. Adjustments in the parameter α (related to the order of fractional temporal derivation) reveal the extent of the memory effect, strongly correlating with fractal properties in the diffusive process. Extending this research to other XRBs is both possible and recommended to generalize the characteristics of X-ray scattering and electromagnetic waves at different frequencies originating from similar astronomical objects.