You can use the Finite Difference Time Domain method "FDTD method", considering your trigonometric equation as a propagation source

you will find attached a code of the FDTD method on Matlab

A triangular wave, that has rising and falling parts, is a continuous function, but a sawtooth, that has an instant flyback, is not.

Sabyasachi Sen : You said " I am asking about continuous valued function not about continuous time function ".

I understand that you are asking if the triangular wave is an analog signal (continuous in amplitude) not asking if it is a continuous time signal.

The answer is yes. Why do you suspect?

Thanks for your kind reply to everyone!

Basically, in my opinion it is a continuous function since at its peak (maxima) left hand limit=right hand limit=functional value although the function/wave consists of two straight line equations one of +ve gradient and one of -ve gradient.

Therefore, the triangle wave has no discontinuous jumps, but the slope changes discontinuously twice per cycle (This is due to the fact that the triangular waveform is formed by two different functions i.e. two different straight lines as their gradients are different ).

Therefore kindly suggest your opinion whether Triangular wave is continuous or discontinuous function/waveform with suitable documents.

Dear Sabyasachi Sen:

I want to clarify two points:

1- Your question is about continuity along time, not along the signal amplitude as you noted in the original question.

2- There is a difference between:

(i) continuity of the function

(ii) continuity of its slope or derivative (which is known as the function differentiability)

The answer to your question:

1- The triangular wave is continuous at all points along time.

2- The triangular wave is differentiable (its slope is continuous) at all points except for its peak and bottom.

The justification is:

1- To be continuous at a point, the function must achieve:

right limit = left limit = function value at that point.

2- To be differentiable at a point, the function must achieve:

the limit: Lim (f(x+h)-f(x))/h is the same from the left and from the right at that point, i.e. that limit exist, or the derivative exists.

There is a difference between a continuous function and a differentiable function. A triangular wave is continuous but not differentiable. A square wave is discontinuous (and possibly double valued!-and if so by definition not a function) as well as not differentiable.