A new method of realizing nuclear fusion reactions based on muon catalysis and the accelerative mechanism is proposed. High-energy ball lightning is periodically generated in a reactor chamber filled with deuterium gas and directed into a container containing liquid tritium. The entry of ball lightning into the tritium is accompanied by the generation of muons and mesomolecules due to a cascade process. Following the ball lightning, a high-energy plasma jet moves under the influence of traveling transverse electromagnetic waves. Deuterium ions and electrons of the jet, accelerated by intense transverse electromagnetic waves, interact with the tritium. Nuclear fusion reactions occur with the participation of muonic molecules at very low temperature. The developed method resolves all physical and technical problems that are inherent in existing traditional methods.