Search

This study unveils the causality between technology innovations and renewable energy in Germany. The discussion about technology innovations and renewable energy is beneficial because the country is most innovative and pursuing ambitious energy transition goals. The results of complete sample causality show that technology innovations significantly impact renewable energy. The rolling window method accounts for structural changes when examining the causal connection between technology innovations and renewable energy. The findings show that technology innovation drives renewable energy positively and negatively across multiple sub-samples. Similarly, renewable energy has a considerable effect on technology innovations in sub-samples, implying that advancement in renewable energy translates into increased spending on technology innovation. The future cornerstones of energy supply comprise fluctuating sources caused by weather which must be balanced out. • Examine the causality between technology innovations and renewable energy. • Explore that technology innovations have a significant impact on renewable energy. • Sub-samples causality is examined while considering structural changes. • Explore that technology innovation is driving renewable energy. • Renewable energy effect on technology innovations in sub-samples. [ABSTRACT FROM AUTHOR]

In this article, we focus on the numerical study of one and two dimensional higher order multi-term time fractional partial differential equations. In the adopted strategy, the temporal fractional derivative is replaced via well known L 1 formula and the integer order space derivatives are approximated by truncated one and two dimensional wavelet series. The fascinating nature of the scheme is to use collocation approach which convert the governing equations to the system of algebraic equations from which the wavelet coefficients can be calculated. Next, stability of the proposed scheme is investigated theoretically which is also the fundamental subject of the current work. Further computational convergence rate is computed which predicts that the order is approximately two. The scheme is applied to solve one dimensional beam models (fourth order partial differential equations) and two dimensional fissured rock models (Sobolev equations). Efficiency of the scheme is examined with the help of various error norms such as I ∞ , I r m s and I 2. Simulations indicate pretty much good results from which we can say that the scheme is suitable and robust for both one and two dimensional problems. [ABSTRACT FROM AUTHOR]