IN THIS PAPER Sinc-GALERKIN method IS USED FOR A CLASS OF TIME-DEPENDENT PARABOLIC EQUATION. THE method BASED ON DOUBLE EXPONENTIAL TRANSFORMATION (DE) AND USED FOR BOTH SPACE AND TIME DIRECTIONS AND IT HAS BEEN TESTED THE ACCURACY OF method ON AN EXAMPLE. FINALLY THE OBTAINED RESULTS BASED ONDE TRANSFORMATION COMPARED WITH THIS method BASED ON SINGLE EXPONANTIAL TRANSFORMATION (SE). THE RESULTS CONFIRM THAT THE ACCURATE NATURE OF OUR method.

IN SOME APPLICABLE PROBLEMS WE CAN OBSERVE SINGULAR INITIAL VALUE PROBLEMS. IN SOLVING THESE PROBLEMS MOST OF NUMERICAL methodS HAVE DIFFICULTIES AND OFTEN COULD NOT PASS THE SINGULAR POINT SUCCESSFULLY. IN THIS PAPER WE APPLY THE Sinc-COLLOCATION method FOR SOLVING SINGULAR INITIAL VALUE PROBLEMS. ABILITY OF THE Sinc-COLLOCATION method IN OVERCOMING ON THE SINGULAR POINTS DIFFICULTIES MAKES IT TO BE AN EFFICIENT method IN DEALING WITH THESE EQUATIONS.

IN THIS ARTICLE WE PRESENT A NUMERICAL SCHEME TO SOLVE THE SECOND-ORDER LINEAR HYPERBOLIC TELEGRAPH EQUATION IN ONE-SPACE DIMENSION. BY EXPANDING THE APPROXIMATE SOLUTION AS THE ELEMENTS OF CHEBYSHEV POLYNOMIALS IN SPACE AND THE Sinc FUNCTIONS IN TIME AND USING THE COLLOCATION TECHNIQUES THE PROBLEM IS REDUCED TO A LINEAR SYSTEM OF ALGEBRAIC EQUATIONS. NUMERICAL RESULTS SHOW THE VALIDITY OF THIS method.

IN THIS PAPER, Sinc-COLLOCATION method IS USED FOR TIME-DEPENDENT CONVECTIONDIFFUSION EQUATIONS. Sinc-COLLOCATION method BASED ON DOUBLE EXPONENTIAL TRANSFORMATION ( DE) IS USED FOR SPACE DIMENSION AND FINITE DIFFERENCE method IS USED FOR TIME DIMENSION. THE ERROR IN THE APPROXIMATION OF THE SOLUTION IS SHOWN TO CONVERGE AT AN EXPONENTIAL RATE, AND THE NUMERICAL RESULTS CONFIRM THAT COMPARED WITH THE RESULTS BASED ON SINGLE EXPONENTIAL TRANSFORMATION (SE), OUR method IS OF HIGH ACCURACY AND OF GOOD CONVERGENCE.

IN THIS PAPER, A NEW VERSION OF Sinc-LEGENDRE COLLOCATION method BASED ON DOUBLE EXPONENTIAL (DE) TRANSFORMATION IS IMPLEMENTED FOR A CLASS OF SPACE-TIME FRACTIONAL CONVECTION-DIFFUSIONE QUATIONS ON A BOUNDED DOMAIN THAT INVOLVE TEMPORAL CAPUTO DERIVATIVE OF ORDER A Î (0, 1].THE APPROACH IS BASED ON THE COLLOCATION TECHNIQUE WHERE THE SHIFTED LEGENDRE POLYNOMIALS IN TIME AND THE DE Sinc FUNCTIONS IN SPACE ARE EMPLOYED, RESPECTIVELY. THE PROBLEM IS REDUCED TO THE SOLUTION OF A SYSTEM OF LINEAR ALGEBRAIC EQUATIONS. NUMERICAL EXAMPLES ARE INCLUDED TO DEMONSTRATE THE VALIDITY AND SIGNIFICANT ADVANTAGES OF THE TECHNIQUE AND A COMPARISON IS MADE WITH EXISTING RESULTS IN THE LATEST LITERATURE.

IN THIS PAPER, WE EXAMINED THE GLOBAL COLLOCATION method USING Sinc BASIS FUNCTIONS FOR NUMERICAL SOLUTION OF THE MODIFIED REGULARIZED LONG WAVE (MRLW) EQUATION. THE PROPAGATION OF SINGLE SOLITONS AND THE INTERACTION OF TWO SOLITARY WAVES ARE USED TO VALIDATE THE method WHICH IS FOUND TO BE ACCURATE AND EFFICIENT.