A Fourier wavelet series solution of partial differential equation through the separation of variables method
Abstract In the present study, a new approach such as Fourier wavelet series solution of partial differential equation through the method of separation of variables has been discussed. This approach includes the process by which the Fourier-wavelet coefficients are calculated, and how these coefficients are used in place of Fourier coefficients to attain the solution. Also, the bounds of these coefficients have been estimated. Convergence analysis and the existence of the Fourier-wavelet series are discussed here. Moreover, it is clearly shown that if the proposed series is exactly convergent, then the Fourier-wavelet and Fourier coefficients coincide. Additionally, the existence of the difference of two equivalent Fourier-wavelet series has been computed. Four illustrative examples have been included to certify the proposed method, which shows incredible performance.